When should we use completing the square instead of the quadratic formula? 👇 kzread.info/dash/bejne/Z41nxriRmcqvcqw.html

@HeavenisnttooFarAway-

5 ай бұрын

What happens to the 25 that you added to the left hand side of the equation?

I have never seen this “box” approach to solving for X before. Pretty cool.

@muneebmuhamed43

5 ай бұрын

btw, the quadratic formula is derived using this. There's a video by "Mind Your Decisions". It's pretty old but explains it well.

@HeavenisnttooFarAway-

5 ай бұрын

Me neither, excellent video

@jaspertyler4557

5 ай бұрын

i learned about completing the square in ordinary differential equations. the most confusing math class i've ever taken.

@samiunalimsaadofficial

3 ай бұрын

Get ready for PDEs​@@jaspertyler4557

@chocolateangel8743

Ай бұрын

It's called an area model. You can use them to do quite a few things. When you understand (and get practice with them), they really allow you to conceptualize things, so there is less to memorize.

Awesome. Thanks for the history video as well. I can see based on this how geometry lead to algebra, and eventually conundrums like "+- √x" that lead to the use of the plot graph solutions & proofs, and eventually, calculus. What a great video! Would love to see more of these historically contentious math terms!

@bprpmathbasics

5 ай бұрын

Thank you so much!

this is the best math channel ever and made understanding the whole completing the square so easily. thank you so much for making these cool videos

This would have made it so much easier to conceptualize in school!

damn who knew that actually explaining the concept instead of just listing steps aimlessly would make me actually fucking learn this concept 😭😭😭 thank you

On point, not too much talking. Great video. Thank you

Thank you thank you sooooooooooooooo much you saved me from the exam

Hey, I love your videos! You actually helped me pass my maths exam with a random exercise, and I thank you alot!! (keep the good work up, love ur channel🔥🔥💯)

Very helpful, thanks

You are the best math KZreadr 😊

This was also visualised in my Mathematics B Edexcel International GCSE study text.

Interesting analysis

This is a neat way of doing it. Of course, you could always do it algebraically, by subtracting 24 from both sides, getting x^2+10x-24, which can be factored out to (x-2) and (x+12), giving us the answers of x=2 and x=-12.

Quadratic solution now kinda makes sense geometrically - it's just a question if I want to add or remove from x square

Thank you, proffesor

you are a genius!

I like to define perfect squares first and then you just use c=(b/2)^2 and see what's extra

The equation i.e ((1/√(x!-1)+1/x^2)! It surprisingly approaches to 0.999. For x>2 lim x→∞ I would really appreciate you if you check it and I would like to ask can this be constant which is mine?

can you please post the solution to sqrt(1/x^2 - 1/x^3) + sqrt(1/x - 1/x^3) = 1 without just squaring both side and making it very long.

@youngmathematician9154

5 ай бұрын

Here is how I did it (it does use squaring both sides but it's not that long, don't worry :)) : First, let t=1/x. Our equation becomes sqrt(t^2-t^3)+sqrt(t-t^3)=1. We will now make a series of algebraic manipulations: Isolate sqrt(t^2-t^3): sqrt(t^2-t^3)=1-sqrt(t-t^3) Square both sides: t^2-t^3=1+t-t^3-2sqrt(t-t^3) Cancel the t^3 terms and isolate 2sqrt(t-t^3): t^2-t-1=-2sqrt(t-t^3) Square both sides again: t^4-2t^3-t^2+2t+1=4t-4t^3 Move everything to the LHS: t^4+2t^3-t^2-2t+1=0 Notice our LHS looks a lot like t^4-2t^3-t^2+2t+1, which we know is equal to (t^2-t-1)^2 since we worked it out earlier. This motivates us to introduce the substitution t=-y. Our equation then becomes y^4-2y^3-y^2+2y+1=0, which factors as (y^2-y-1)^2=0, which is equivalent to y^2-y-1=0. Solving this quadratic equation gives us y=(1+-sqrt(5))/2. Since t=-y=1/x (our substitutions from earlier), we have x=-1/y. Therefore, x=-1/((1+-sqrt(5))/2)=-2/(1+-sqrt(5)). Rationalizing the denominator gives x=-2/(1+-sqrt(5))*(1-+sqrt(5))/(1-+sqrt(5))=-2(1-+sqrt(5))/(-4)=(1+sqrt(5))/2. Hence, x=(1+sqrt(5))/2 or x=(1-sqrt(5))/2. However, we have to reject the second solution since it makes the second square root in the original equation a complex number. Therefore, the only solution x=(1+sqrt(5))/2, which just so happens to be the golden ratio!

im not confused any longer

And now I'm confused

... Und jetzt noch den Zusammenhang zwischen x=2 und der Abbildung... bzw x=-12 und der Abbildung 😮.....

why do we always assume that x is greater than the number?

@zemyaso

5 ай бұрын

Graphs are not gonna be 100% accurate. If x was or = the number, then just draw the x accordingly. This is just to get the idea of where completing the square comes from.

@channelbuattv

5 ай бұрын

@@zemyaso When people draw (a±b)² sometimes they assume either a>b or a

@bprpmathbasics

5 ай бұрын

It doesn’t matter. I could have done a smaller square first then a bigger one. 😃

@channelbuattv

5 ай бұрын

@@bprpmathbasics Divide by 2 or multiply by ½?

! warning do not trust this guy !