This is also worth checking out: "New" Way To Solve Quadratic Equations That Everyone Is Talking About : kzread.info/dash/bejne/oYt6tLdmpc_HXaQ.html Professor Po-Shen Loh devised a different way to solve quadratic equations that could be helpful to many students.

@swagbhai1511

4 жыл бұрын

No bro factor method is so good and if he not work quadratic formula always worke

@Elly5955

4 жыл бұрын

You're so good in math, thank you for the explanation.

@TheOofster123

3 жыл бұрын

X^2 +2X+1 = (X+1)^2

@dskinner6263

2 жыл бұрын

The "couple of steps" you skipped in the second half of the video is what I came here to understand. It's been a long time since I studied math, and even my arithmetic is rusty when it comes to subtraction of fractions that include variables. Can you please point me to where I can learn why (-c/a)+(b²/4a²) = (b²-4ac)/(4a²), step by step? I remember it has to do with cross-multiplication, but I'm not getting it. :-(

@ccbgaming6994

2 жыл бұрын

You just multiply the term to make both have a common denominator, so here it would be by 4a

I've been using that formula for over 40 years and until now I've never wondered where it came from. Thanks for the enlightenment.

@DaveScottAggie

8 жыл бұрын

Yes. 38 years for me. While the (negative lengths) kind of throw a wrench in, overall seeing it as matching up equal areas makes it easier to grasp.

@ghanshamchandel1854

7 жыл бұрын

i used it for about 2 years and i knew it a year ago!

@hugofontes5708

7 жыл бұрын

half way through an engineering major and didn't have a clue until now, I just used it until I got used to it

@michaelkarnerfors9545

7 жыл бұрын

28 years here... and I am completely mind-blown. So amazingly intuitive!

@DerToasti

6 жыл бұрын

the way it's usually derived is pretty simple though.

This video should be presented in every high school and middle school algebra class.

@billstokes9645

8 жыл бұрын

+Benny Doe I agree, I do hope students share this with one another. I taught high school math years ago, I never made this as clear as the video does in less than ten minutes! Bravo.

@dragonite7780

8 жыл бұрын

+Bill Stokes I thought I'd just tell my maths teacher, so that when he teaches gcse he can show this to his students so they can hopefully understand it better and not think 'its magic' or similar things.

@Peter_1986

8 жыл бұрын

This is how math should be taught. I see too many math teachers who just present formulas out of nowhere without actually deriving them and explaining them, and this is pretty much like giving an instruction booklet to a beginner and ask him/her to use that booklet for everything. Yes, there are situations when certain topics might be useful and important but also too complicated to actually derive at that point, but if something *can* be derived without too much trouble then it *should* be derived. One rule of thumb is that students should be able to reprove those formulas to themselves with absolutely no extra help or reminders - everything should come from logical step-by-step reasonings.

@gregoryharlston3989

7 жыл бұрын

As a new math teacher, I'll definitely be using this.

@hustler3of4culture3

7 жыл бұрын

+alejandro cartes you can also tell your teacher that this is the same ancient method that Al-khwarismi used in around 820 ad in his compilation of algebra techniques. this geometric method has been around for millennia.

Gosh why didn't the school teacher explain this theorem in this illustrative manner. God bless you Sir 🙋☺👍.

@troubledsole9104

7 жыл бұрын

Because the school teacher doesn't have a strong math background; but you probably knew that.

@rickwhite4137

7 жыл бұрын

I was going to ask the same question.

@muhammadkhairul2794

7 жыл бұрын

They gotta understand the concept that 'x' here doesn't refer to length but rather simple algebraic, since this is just a geometric illustration of quadratic formula to enlighten us

@vasilisprotopapas2447

7 жыл бұрын

Coma White nn

7 жыл бұрын

They either don't know it themselves or they don't know how to teach. But, as far as my knowledge goes... Kids usually don't understand math because they find it boring as kids usually don't have to use math very often in a concentrated way and that requires a little thinking (outside of school grounds). So, whenever they teach this, you are a 10 year old kid with almost no knowledge of algebra. So, despite trying to understand the visual part, you miss the opportunity because you lost yourself in algebra. And there is that game kids are playing so.. You probably paid zero attention. Why am I saying it? Because it is in curriculum and in almost every math book for kids in age ranging from 8 to 12. I, of course, can't guarantee this considering the USA. In my country at least, every kid is supposed to know this despite they don't: too poor to study (should be a motivation), no interest, no teachers.. But the books do cover it.

I really enjoyed this video. Years ago, I was in college, majoring in Mathematics, with the goal of becoming a math teacher. My ultimate goal was going to be the teacher who spotted the "hole" in a student's understanding of mathematics, transforming them from a math-phobic student to a math-master student (as was done for me by a wonderful teacher in high school.) Since the field of math is cumulative, knowledge wise, any area not completely understood by a student in the past, will ultimately become an abyss in the future. Sadly, a TBI ended my progress in college, but with the help of KZreadrs like you, I am re-discovering my love of mathematics. Who knows? Maybe I can tutor some students one day. Thanks!

@primeirrational

7 жыл бұрын

Frank De Mascio it's never too late to live a dream!

@RushuFriends

7 жыл бұрын

Frank De Mascio I love your comment

@lnopia

7 жыл бұрын

I hope you get the chance to tutor some kids, you sound like the ideal math teacher!

@teev7

7 жыл бұрын

Frank De Mascio wow! You moved me to tears. Thanks for your inspirational comment!

@jarencascino7604

6 жыл бұрын

Frank De Mascio I hate how teachers use acronyms and such. What they do is give you a shortcut without actually getting the deep understanding you need in the future.

Wow. 'Completing the square'. Well, I'll be damned, that's exactly what we're doing.

@NY4realz

7 жыл бұрын

thats what i was thinking

@Forza_Europa

7 жыл бұрын

100th like. Completing the 10th square ;)

@saptarshi4105

5 жыл бұрын

1 year since this comment.. Did it work?

@angelmendez-rivera351

5 жыл бұрын

Andrew Goering Proof of your statement?

@alexwang982

5 жыл бұрын

Duh

I never liked mathematics when I was in my younger age because most of my teachers presented it arbitrarily and non-chalantly, devoid of passion and wonder. Now, in my late 30's, I'm hooked on it because of great math channels like you. Can you do a series on millenium prize problems? Also: Hilbert's problems, Continuum Hypothesis. Thank you!

One square to another: "You complete me."

@nilefield8910

3 жыл бұрын

The Dark Knight? :D (I’m from the future :P)

@awaken6094

2 ай бұрын

Lobotomy kaisen

I love how simple he makes it all look, by using a calm voice and great representations. And Desert Cactus you are right, this should be shown in every high school and middle school algebra class. I teach adult ed, and they need to understand algebra to get their HiSet or prepare for the test to go into college, and this is yet another excellent video from him.

why the fuck have i never encountered a teacher who has taught this?

@omargoodman2999

7 жыл бұрын

You have. When you watched this video.

@ianjohns109

7 жыл бұрын

Omar Goodman haha that's a good point

@johnconway8070

7 жыл бұрын

I taught the derivation of the general quadratic formula 25 years ago to Intermediate Certificate students (c 15-year-olds) here in Ireland. Later, a revamp of the syllabus no longer required that students be able to *establish* the formula at IC Level, merely to be able to *apply* it in cases where the constants had specific values and the discriminant was > 0 or = 0 . We did not use the rectangles and squares method but rather completed the square by taking half the co-efficient of x , squaring it then adding this squared quantity to both LHS and RHS etc.etc.

@KAF128

7 жыл бұрын

We did it exactly as you (and PT) said at secondary school in England in the late 70s - but I had forgotten how to derive it, so I'm pleased to see this !

@SmallSpoonBrigade

7 жыл бұрын

Because you have to teach students how to complete the square in order to do it and completing the square is only used for this and converting quadratic equations into the vertex form. Consequently, you can save a lot of time to do other more useful things if you're not required to cover the vertex form.

I can think of a lot of people who could've benefited from this means of demonstration; much more straightforward and powerful than just forcing them to memorize the quadratic formula.

@AngieMyst

8 жыл бұрын

We were taught this visual method to explain the formula in Algebra 2, but I don't think a lot of people made the connection or preferred to think in terms of numbers instead. I like this method the most.

@Minecraftster148790

8 жыл бұрын

I find that u just remember it and then it is impossible to forget it

@dekippiesip

8 жыл бұрын

+AngieMyst I knew about the algebraic derivation, but didn't connect it to anything geometrically. While geometry is much more intuitive in most cases, I think we can learn a lot from the ancient Greeks when it comes to this, as they connected nearly all mathematics to geometry.

@ydela1961

8 жыл бұрын

+Cubik What kind of math teacher does that? In school all of my math teachers always gave the full explanations of all formulas we learned. We were not forced to remember the explanations as for the test only the formula was required. Most of my classmates memorized only the formulas, but I assure you, we had always the complete explanations. For me, memorizing a formula with no logic was a greater effort than remembering the (logic) way to get there. In a lot of cases because of poor memory, I did not remember formulas for the exam and I had to reconstruct them. That was easier for me that way. I was always in the 3 best students of my class in math... never knowing the formulas, always able to reconstruct them. So I guess in your class, with your teachers, I'd been in the 3 worst math student.

@AgentMidnight

8 жыл бұрын

ydela1961 Congrats, I guess

At the time (1973), I thought my 8th grade Advanced Math and my 9th grade Algebra teachers did a fabulous job of presenting the quadratic. I'm willing to concede that this is better. Very well done. 5 stars.

Everyone made fun of me using completing the square in 12th grade, whilst they were using the quadratic formula - they said I was wasting my time. I believed it was a lot more elegant. So I decided to prove to them that it was the same thing during one of my classes near the end of the year... took me forever - but I eventually got it. IF ONLY I knew this. SUCH an elegant proof - great video explaining it!

@yashuppot3214

5 жыл бұрын

Yeah more elegant but y consume more time

@sunjidasultana4648

Ай бұрын

I prefer factorization more than the formula or the completing square method

that makes a whole lot more sense now. thank you

@docdaneeka3424

7 жыл бұрын

I did 'completing the square'in school over 15 years ago. I went on to do an engineering degree, and a degree in pure mathematics. I wish my maths teacher in school (who was a really good teacher) had explained completing the square and the quadratic formula this way!

@f.demascio1857

7 жыл бұрын

Doc Daneeka Many students wish the same thing. Often times, approaching a problem with a visual example like this can blow open doors for students who "just don't get it."

@brendan2868

5 жыл бұрын

And often times it can just confuse them further..

@donlansdonlans3363

4 жыл бұрын

@@docdaneeka3424 how do you get a degree in pure math without knowing this? XD

@Surfing566

3 жыл бұрын

@@donlansdonlans3363 no, they knew how to complete the square, they just didn't know the proof behind it

me: cool wow im understanding presh: im gonna skip a couple steps me: what no

@ghoulslayer4066

5 жыл бұрын

shy bound literally me, lmao

@laikaperraespacial6025

4 жыл бұрын

Itbwas multiplication of divisions CD

@whalestailz

4 жыл бұрын

@@laikaperraespacial6025 how does 2a * root 2a^2 become 2a again in the final formula? wouldn't the 2a become another 4a^2 under the radical meaning it would end up as a 4a^4 after it's square rooted in the final form? based off his explanation

@laikaperraespacial6025

4 жыл бұрын

@@whalestailz nop

@aaronbell5994

4 жыл бұрын

The Khan video doesn't skip the steps kzread.info/dash/bejne/n3ihtLufncSfc5M.html

I was just realizing that I have followed every explanation you’ve every given on your channel with a minimum of effort. That’s what makes you a great teacher, and that explains why I keep coming back.

Wonderful. No teacher or Prof ever explained this. Just memorized and used it. Thank you.

You are a much much better teacher than the current average math teacher or any normal math book. I've been following your vids for quite a while now, and they really motivate me to learn and understand more about math. Thank you!

This was really terrific. You did such a good job bringing us along and the visuals were super clear. Thanks for doing this!

Ok this is awesome. I've read on school books that the proof of the quadratic formula was too hard, but this is very simple and ties in with the concept of completing the squares. And you can even show it with pictures, for people that easily loses track of numbers.

This is one of the best videos on youtube. I am in grade eight and had no problem keeping up due to your amazing visuals and your simple explanation of the concepts. I look forward to using the quadratic formula with the understanding of how it came to be!

@JawnBoyd-rt9gd

5 ай бұрын

Did you?

@ManBro25

5 ай бұрын

Did you ?

I was struggling to teach some of my students the quadratic formula and I started thinking about it in similar terms such as this (minus the part about negative lengths). I knew some of my students might find this confusing. However, I took a chance and tried explaining the quadratic formula to my students in this way. For several of my students, I could see light bulbs going off--they got it! However, for many of my students, this only confused them further. I like your video. You explained it much better than I think I did (the colorful virtual manipulatives you used are extremely useful), so I think I'll be showing my students this in the future. I am a new math teacher and I try so hard to teach my students an intuitive way to think about math, like this for example. But sometimes, it seems that I only confuse them more. Also, if you've never been taught to think about math intuitively, then thinking intuitively requires a different orientation--kind of an undoing of just memorizing stuff to get answers. Keep up the great, great work!

@eric_enter9141

5 ай бұрын

Legend. Hope you had 7 good years since you commented this.

@tramothithanh2429

5 ай бұрын

vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_b%E1%BA%ADc_hai

@PatrickCraig-lh5is

3 күн бұрын

Another piece of this is relevance to students' lives. Sure, "real world" applications utilizing the quadratic equation are everywhere, but in most cases students will counter with, "Yeah but I won't be using this in my own life, so why learn it?" For example: lobbing a basketball and modeling its motion with a quadratic might seem an ideal motivator, but how often do you see LeBron James out on the court with paper and pencil calculating the ball's trajectory? My own solution to this was to create a 2-D basketball simulator in the Scratch programming environment; players input a "best guess" angle and initial velocity and watched the results. This can springboard into a discussion of the math behind why the ball did or didn't go into the basket. We need to really put our backs into the relevance aspect of math. It's important.

Wow. I have been searching the exact reason behind this quadratic formula to work. I finally found it

I am so glad I watched the proof at the end. Holy Cow! NOW I understand the HOW and WHY.

@putteyu29

7 жыл бұрын

same här dude, :))) I had this quadratic completing thing a years ago, now i am really understanding it

@marknudelman1122

7 жыл бұрын

Joe Edwards Same Mind Blow

Just letting you know, once again, how much I love your videos. This was so well done. Empowering! I hope I get the chance to teach the quadratic equation to my grandchild using exactly this video!

I can't thank you enough! The visual representations make it so much clearer!

This video blew my mind. I always wanted to know where the formula comes from, and know I got it! Love your videos :)

Visual presentations always make so much more sense to me, thank you for this great concise presentation! 👍

I've never thought about understanding quadratic equation in this way.Thank you so much for making this video.

@anymaths

4 жыл бұрын

watch my useful mathematics videos.

I am giving you the biggest like I have ever given on KZread!!! Thank you for enlightening one great frustration from an elementary school.

@elyseemutha8956

6 жыл бұрын

Petrhrabal

Great video! This is the most excellent description of a very complicated concept I have ever seen.

Your visual explanation is terrific! Thank you.

after all those years, finally a visual explanation of how, and why, the expression "completing the square"

The first time I saw the algebraic derivation of the quadratic I thought I was gonna cry, but this was even more sublime. Nice work keep it coming.

@edithisaok580

6 жыл бұрын

x=3

This was an amazing video! For the first time, I really understand the real meaning of the quadratic formula. Thanks

I learnt about quadratic formula in 1983 and only today I can visualize where the formula come from. Thanks for the enlightenment.

That was fantastic! Extremely visual and clear to understand!

he made me understand it in 10 mins what 2 years in my school couldn't

@guitarraccoon1541

5 жыл бұрын

But if you don't understand it then you haven't learned it, which goes against the very idea of schools.

@dirktween244

4 жыл бұрын

How about 30s ?

Why there's no one like you to teach these mathematical concepts so easly at schools?

This is gold. I can't thank you enough. Now everything is clear and not boring

It's just amazing, 27 years after I've learned this I discover this video, just great job. Thank you!

Interesting and amazing. And I had to memorize deriving the quadratic formula the hard way. Thank you, sir.

@karineaudet6270

Жыл бұрын

Good as akways but i asleep

Bro, your channel is going to help so many unsure geniuses to unleash their geniusity 🤣 Love you, keep the good work!

@mathfullyexplained

3 жыл бұрын

Try my channel mathfullyexplained

I remember showing my son who just learned completing the square how to derive the quadratic equation at the kitchen table. I got more and more excited as I progressed. My son and daughter just looked at me like I was crazy.

The complete explanation for the completing square which all high form students of the secondary should learn deeply by heart and digest the logics and inference. Excellent!

tbh, watching this make me realize how unreal or imaginative the negative numbers are. How do you even picture a negative number.

@MrRight-jl5dt

4 жыл бұрын

Just picture an overdrawn bank account :) .

5:10 you could've explained this as when square rooting both sides you will go from (x+1)²=16, to x+1 = [+/-]4 because when square rooting, you get a negative and postive value. I just thought giving the length a negative value is quite confusing as that's quite impossible..

@tramothithanh2429

5 ай бұрын

Definitely true. Ancient Babylon peoples, only positive, negative or complex solution, Value. Virtual+real with i. vi.wikipedia.org/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_b%E1%BA%ADc_hai diendantoanhoc.org/topic/169871-gi%E1%BA%A3i-ph%C6%B0%C6%A1ng-tr%C3%ACnh-b%E1%BA%ADc-2-b%E1%BA%B1ng-ph%C6%B0%C6%A1ng-ph%C3%A1p-h%C3%ACnh-h%E1%BB%8Dc/

Very clear and precise teaching. This is by far the best explanation of completing the square method to solve quadratics on YT. Thanks brother!! ❤

Spoken clearly and explained well. Great video, thank you!

In our school: They give the equation and say solve a few sums using it fast, so that we can complete syllabus for EXAMS.

@anymaths

4 жыл бұрын

my videos help your school works.

@kabirchatterjee1157

4 жыл бұрын

tatakau heroooooooooo!

OMG! I can't talk English very well, but I got it throughout the video and I could understand to solve that problems! Thank you very much... +1 subscriber

This was really helpful! Thank you so much for the explanation!

Great video! Great graphic explenation! As always, your explanations are simple and clear. Ty for exellent video.

That's awesome to have a graphical representation of completing the square. I learnt the algebraic way to solve quadratic equation in my high school but never have thought this could be done using geometry. I wonder if this method also works on solving cubic equation.

@thomasbassil140

Жыл бұрын

It does, i forgot how but i've seen it done

Thanks lot now I understand much more about it and how it actually works! Thanks love it!

I'm honestly just sending this to my Maths teacher as something to show people in the future even if it isn't my class as we have moved on topic wise, but still as something to help others in the future

This was truly brilliant. I learned to complete the square 54 years ago, but I never realized how it was derived. This should be presented in every high school algebra class. Thank you so much for this and your other videos.

This explanation would have been nice to have 15+ years ago back in Grade 8. I was just told the formula, and that was it.

@bassemghorab

5 жыл бұрын

@Fester Blats Only if he's a sheep like you. People go to school to understand, not just use things without knowing anything about them

@brendan2868

5 жыл бұрын

You probably still wouldn't understand it at that age and level even if it was explained geometrically or non geometrically

@julliferjosephtuba2202

4 жыл бұрын

@Fester Blats I do find that the beauty of maths isn't the solving part, but it is understanding the logic behind every step. Appreciating logic is found in maths, and this same appreciation of logic can apply to other aspects of life beyond maths as well. For example, if you have a strong foundation and appreciation of understanding mathematical proofs, Surely, you wouldn't be as gullible to propaganda and conspiracy theories in real life as you would be meticulous towards the proofs and evidences behind them, skills you've honed through scrutinizing mathematical proofs.

This makes me want to try the same thing with a 3rd degree polynomial to see how it turns out! ;)

@turbopotato4575

6 жыл бұрын

Dont. I filled 80 pages of my A4 size exercise book doing that

@prashant_kissago

6 жыл бұрын

you will need a 3d model for that. a 'cube' they say...

@harmitchhabra989

6 жыл бұрын

You will end up with what is called THE CUBIC FORMULA

@mastercraft117

6 жыл бұрын

Try it with a 5th degree polynomial

@nicolasrenard2551

6 жыл бұрын

There is no general formula for roots of polynomials of degree higher than 4 (Galois' law)

That here is the most satisfying video I've seen in a very long while!

Wow, man. You open my eyes, your job is amazing!

The name "algebra" comes from al-khwarizmi book. In that book, he shows quadratic solutions in that way. So that is the way it has been done since the beggining =P But mr Khwarizmi doesn't considered negative values, so he split the quadratics in 6 different types. I didn't like the way you does it. I'm gonna show that example for my students though. Sorry for bad english :)

@robertgumpi7235

5 жыл бұрын

Arley Antes wasn’t it Euclid in the Elements?

4:55 the mystery length of -4

@francistan4674

4 жыл бұрын

Negative quantities have physical meaning. Think negative displacement, negative velocity and acceleration. Going further, even "imaginary numbers" have real meaning in the physical world.

@stevezelaznik5872

4 жыл бұрын

Imagine the trajectory of a cannonball. The quadratic formula tells you the positive answer, when it will hit the ground, and the negative answer, when and where in the past it was shot out of the cannon.

@dirktween244

4 жыл бұрын

What is a box with a side of -4 ?? -4 is not wrong ! The use of the equation, IS wrong ! As noted by others, it could mean: Before your determined start time !

@nepasdisponible

3 жыл бұрын

@@francistan4674 But this is completely different from what you've told. This one deals with negative length.

@asr2009

Жыл бұрын

@@francistan4674 yes. but length or distance is a scalar quantity so cant be represented by negative numbers. this is why separation of algebra and geometry is important.

Great video! Best clarification of completing the square that I’ve seen.

Excellent explanation and I think necessary for all the visual learners like myself.

Wow, that's something our teacher never said to us :) Time to impress him :D

Marvelous presentation, thank you Presh!

Brilliant! I honestly can say I have never seen this explanation before. Now I know where the quadratic formula comes from. Thanks!

Crystal clear! I would have loved to have such a brilliant math teacher!

Impresionante!! Se siente tan bien entender de una forma más profunda a una ecuación que a primera vista parece bastante complicada, es tan simple que no entiendo porqué no lo enseñan así en el colegio, de verdad, todo es memorizar formulas resolver ejercicios y dar examen, pareciera que están fabricando robots. Gracias por esta explicación! Saludos desde Perú.

@liliacfury

6 жыл бұрын

Translation: (Esta es una traducción del español al inglés) Awesome! It feels so good to understand in a more profound way to an equation that at first glance seems quite complicated, it is so simple that I do not understand why they do not teach it thus in the school, really, it is all memorizing formulas to solve exercises and to give examination, it seems that they're making robots. Thank you for this explanation! Greetings from Peru.

@liliacfury

6 жыл бұрын

Albanovaphi7 Eso es muy cierto, siento que el sistema educativo no está actualizado con las necesidades actuales de educación y crecimiento para los humanos. Algo tiene que cambiar Saludos desde América.

@samuel7998

6 жыл бұрын

Más profundo no se traduce more profound, se traduce deeper. En do not teach it thus in the school, el thus sobra y es this, no it. En "examination", eso es incorrecto, lo correcto es test para referirte a un examen escolar. Se que es muy tarde ya xD pero mejor tarde que nunca.

@angelmendez-rivera351

5 жыл бұрын

Históricamente, las escuelas existen para fabricar trabajadores humanos que operarían como si fueran robots. El que te dijo que uno va al colegio a aprender no sabe nada de historia.

Really clear and detailed. Fantastic for understanding!

This is the best video on 'completing the square' on all of internet both graphically and algebraically.

this video was MOST EXCELLENT..!!!... I've never seen this kind of explanation for the Quadratic Equation....... it's amazing how the Visual of the Geometry can really Convey the logic of math proofs... THANK YOU!!...

@daledo8604

7 жыл бұрын

kicsimoe there was a time we learned from books, not wiki! 😂 I've never had the privilege of seeing this done visually either.

@abhitechno

5 жыл бұрын

Philip Y nice

@rajeshpatley7564

5 жыл бұрын

बहुत अच्छा वीडियो है पूर्ण वर्ग बना कर हल करने का ज्यामितीय तरीका बहुत बहुत धन्यवाद आभार

Can you similarly 'complete the cube' for the general cubic equation? And, although it's difficult, if not impossible to visualize, 'complete the tesseract' for the general quartic equation? Do any of these visualizations... those that are possible... provide any insight into why you can't solve the general quintic equation and higher with radicals?

@blangoog

8 жыл бұрын

I think the hard part there is that, once you get to 4th degree polynomials, visualizations kinda break down. Maybe someone could think of a clever way of still showing it intuitively, but at that point in kinda just comes down to proofs Also, I think it's probably a mistake to ever be using the quartic equation... that thing is a mess

@dekippiesip

8 жыл бұрын

+Daisy Bell and to top it off, show geometrically why this trick fails with the 5th degree polynomial using a 5 dimensional 'cube'.

@dekippiesip

8 жыл бұрын

***** but you could still use it since it is possible to do math on objects of any dimension. The difference is that you use geometric methods instead of algebraic ones to prove a point, even if the geometry requires more than 3 dimensions.

@dekippiesip

8 жыл бұрын

***** I agree, it could still be used as an alternative to an algebraic proof but it will loose some of it's pedagogical value. Maybe it will be easier than the algebraic proof, maybe it will be harder. But it certainly won't be as easy as the n=3 or n=2 case.

@samisiddiqi7814

6 жыл бұрын

Imagine completing the hypercube.

As a student of a quite basic math course, this explained alot. Thank You!

This is one of the videos the internet was built for. Thank you!

I was taught this 45 years ago as completing the square without the geometric representation. It of course leads directly to the quadratic equation and that was why we were taught the method rather than simply using a formula with no idea how it came to be. Education used to be called teaching and teachers were effective. Now we have "educators" and all sorts of theory about teaching and no common sense. Oh dear, I'm getting old.

@FinnMcRiangabra

8 жыл бұрын

+984francis At the risk of igniting internet rage, I am going to propose that partly this is an unintended consequence to employment equality between men and women. Once upon a time, women were very restricted in employment opportunities. For white collar work, it was pretty much: secretary, nurse, teacher. Smart women probably went into those fields (rather than into unskilled work). Smart women are as smart as smart men. Thus you have women with doctorate-level intelligence doing these jobs. I suspect that we used to have hidden high-achiever women in admin assistant, nursing, and teaching positions that now have moved out to better paying positions. It is good for them, but bad for the rest of us.

@MKD1101

7 жыл бұрын

as long as I am getting laid, I don't care about equality or inequality.

@BTGTB

6 жыл бұрын

Mark M. That is a point I've never thought about. I grew up homeschooled and now work a job as a math tutor, so I get questions regarding my opinion of the public school system all the time, and why it now sucks. This makes sense as a contributing factor: the majority of teachers are actually just dumber than in times past. Thank you.

@brendanmccann5695

6 жыл бұрын

and your evidence for this is .....?

@abijo5052

5 жыл бұрын

BTGTB Smarter teachers don’t equal better teachers though. I’ve been taught be people with PhDs and those with bachelors and the PhDs have never been very good. Because it’s easy to them, and they would rather be at a university.

So here is my Solution (an easy one): First I added 15 on both sides, leaving me with the equation x^2+2x = 15 Then, I added +1 -1 on the left side, so it said x^2+2x+1-1 = 15 Then I used the binomic formular (is that how you call it in english?) (x^2 + 2×1×x +1^2)-1 = 15 --> (x+1)^2 -1 = 15 Then I added one on both sides (x+1)^2 = 16 I took the root x+1 = 4 or x+1 = -4 And finally, I subtracted 1, which lead me to x=3 or x=-5 I think this is an easy solution, using basic mathematic formulars. I'm sorry for my bad english, i'm from Germany (ze state where zey can't pronounce ze words correctly) 😉

@user-xr1rf8sj8e

4 жыл бұрын

Your English is actually pretty good. It's just that you spelt a word wrong. It's formula, not formular.

@francistan4674

4 жыл бұрын

You're missing the point. He explained how to derive the quadratic formula. He wasn't explaining how to solve for x, which is what you did.

@prashantaoram7777

4 жыл бұрын

He is explaining why we are doing this.

@arifkulkarni163

4 жыл бұрын

Its *BINOMIAL FORMULA* btw..

@mathfullyexplained

3 жыл бұрын

Add 1 to each side. Factor left side as ( x+1)^2 then use square root property. Try my channel mathfullyexplained. Full unit on solving quadratic equations plus more units

I have subscribed over and over , what an eye opener

Thanks. Your videos sooth my soul. I can feel numbers or the equations.

Wow. I swear to god I would NEVER expect to see Bhaskara being formulated at the end. Initially, it seems such a surreal formula, but when you look at step-by-step you realize why it makes so much sense.

As an engineer, I refused to memorize this equation my entire life because the teachers wouldn't tell/know where it came from.

@jesonroy1932

3 жыл бұрын

Even teachers can't visualise this

@mathfullyexplained

3 жыл бұрын

Try my channel mathfullyexplained. Full unit on solving quadratic equations plus more units. Explains how quadratic formula is derived after completing the unit on rational expressions

@tomgreene2282

3 жыл бұрын

Why are quadratic equations so important....what drove the quest for solutions?

One of the most valuable lessons on the subject! Thank you, sir!

@mathfullyexplained

3 жыл бұрын

Try my channel mathfullyexplained. Many units

this is the best explanation of this concept I've ever seen.

The video was very intuitive. But can you please explain the geometrical meaning of negative value of x

@barfyman-362

7 жыл бұрын

Pranav Kumar S. I think of X times X as adding X number of X spaces I think of -X times -X as removing X spaces of -X. basically like if there was some object taking up space, you are removing this "negative space". in other words multiplying positive numbers is like adding another room to you house, while multiplying negatives is like clearing out a full room so you have more space. either way, both give you more space.

@angelmendez-rivera351

5 жыл бұрын

There is no geometrical meaning to having negative side lengths. There is a reason negative numbers are almost never used in geometry.

you should do it for the cubic and quartic equations formula

@Woodside235

8 жыл бұрын

Hour and then a day long video, respectively.

@uhbayhue

7 жыл бұрын

lol

@zelda12346

7 жыл бұрын

And then explain the proof as to why there is no analytic formula for degree 5 or more.

@marek.p

6 жыл бұрын

xapoliz vieira "complete the cube" and "complete the tesseract"? :P

@user-nm4ni5us8j

5 жыл бұрын

x^3-6x^2=0 x^3-6x^2+12x-8=12x-8 (x-2)^3=12x-8 You have to add a x-term in the right side and because that it does not "works like a magic" with cubes.

That is the best demostration of the quadratic formula I've ever seen.

BROOOOOOOOOOOOO HELL YES!!! Finally understood the intuition behind it. You know how school is they just tell you to memorize it without even bothering to teach you where it comes from !!

This is the beauty of math

I though that I will just need to answer “3” when I was looking at the thumbnail cuz 3^2 + 2*3 = 15

@chellurivenkatasatyanaraya240

3 жыл бұрын

Very nice reply but you are a learner of fundamental mathematics or master of mathematics or teacher of mathematics immaterial,we are all in one family we want to need support each other because we want to create a good human society.:-CHVSN as a INDIAN mathematician till I am a learner of fundamental mathematics.

Brilliantly explained to make it easy to understand... Thank you..

Perfect explanation on 'completing the square'!

woah wait. I got everything up to the last part. how do you simplify x= -b/2a plus-minus √b^2-4ac/4a^2?

@Mycroft616

7 жыл бұрын

The square root of 4a^2 is 2a (as well as -2a, but we're ignoring that), so we can simplify the bottom and restrict the square root to the top of the fraction. This gives us a common denominator and permission to combine the fractions.

@mayagusak3748

7 жыл бұрын

+Mycroft616 oooh I didn't know that you had to root the denominator too. thanks for clearing that up

"im going to skip a few steps here..." Stop. Wait a minute. Fill my cup, put some explanation in it. So a magically jumps to the top and and is multiplied by 4?

@ongshenghao8827

8 жыл бұрын

-c/a becomes 4a(-c)/4a(a) to get a common denominator of 4a^2

@hotdogskid

8 жыл бұрын

oh that makes more sense

@gerald02121

8 жыл бұрын

+Ong Sheng Hao He still should have taken 10 seconds to show that, would have made the video a lot more complete.

@benjamingoldstein14

6 жыл бұрын

He doesn’t need to show you guys how to add fractions

@marklowery863

5 жыл бұрын

Lame Bruno mars reference

THIS IS THE BEST THING IVE EVER SEEN OMG GOD BLESS YOU

I love the background music, it is really concentrating.

is your name fresh-talc-water ??????????

@5dudelsack5

7 жыл бұрын

Presh Talwalker

@yanivshemtov9430

7 жыл бұрын

oh

@branthebrave

7 жыл бұрын

fresh tall walker

@wanyinleung912

7 жыл бұрын

Pressure locker

@unlincecosmico6192

6 жыл бұрын

flesh chop worker

This method was first introduced by Al-khwarizmi, the father of Algebra, near 1000 years ago! could you believe that?!

@Argdut1106

5 жыл бұрын

No.. this was given by Indian mathematician Sridhar Acharya even before that. It's his formula :)

@dyer308

5 жыл бұрын

@@Argdut1106 Even before him, The Babylonians knew about this lol, But Al-Khwarizmi can be called the true father of the Quadratic equation since he was the first to put it in modern notation, combing its geometric/algebraic interpretations, exploring range and methods of obtaining all solutions, as well as applying it to finance and trade

@ubaidshah1910

5 жыл бұрын

Arghya Dutta The person youre talking about is ayrabhatta, and no even he didnt invent algebra, it was known at babylonian times. Stop crediting everything to india

@ambrishabhijatya7842

5 жыл бұрын

@@ubaidshah1910 Have you even read Al Khawarizmi ? Every single one of his books explicitly credit previous Indian mathematicians and that too in the title rather than in the footnotes.

@debgupta1

4 жыл бұрын

@@ubaidshah1910 You are too innocent.He is talking about SHRIDHAR ACHARYA not ARYABHATT. Both were different.

Really great sir. Many thanks for sharing your knowledge and explaining so impeccably. God bless you.

I’m so grateful my teacher explained it this way.