When should we use completing the square instead of the quadratic formula? 👇 kzbin.info/www/bejne/a4qWlYmOnsx8eKs
@HeavenisnttooFarAway-10 ай бұрын
What happens to the 25 that you added to the left hand side of the equation?
@earlthepearl392210 ай бұрын
I have never seen this “box” approach to solving for X before. Pretty cool.
@muneebmuhamed4310 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-10 ай бұрын
Me neither, excellent video
@jaspertyler455710 ай бұрын
i learned about completing the square in ordinary differential equations. the most confusing math class i've ever taken.
@samiunalimsaadofficial8 ай бұрын
Get ready for PDEs@@jaspertyler4557
@chocolateangel87435 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.
@MurseSamson10 ай бұрын
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!
@bprpmathbasics10 ай бұрын
Thank you so much!
@Monitorbread7 ай бұрын
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
@kambaakapanga96297 ай бұрын
On point, not too much talking. Great video. Thank you
@EverythingIsLit9 ай бұрын
This would have made it so much easier to conceptualize in school!
@ratty_robloxian8 ай бұрын
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🔥🔥💯)
@EdwardCurrent4 ай бұрын
Brilliant explanation. I'm so jealous of kids today -- and teachers today! -- who can get these great explanations and learning methods at home for free. This geometric demonstration reminded me of 3blue1brown's geometric treatments of linear algebra. So cool.
@rigbyb10 ай бұрын
You are the best math KZbinr 😊
@AzureKyle6 ай бұрын
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.
@SeegalMasterPlayz10 ай бұрын
This was also visualised in my Mathematics B Edexcel International GCSE study text.
@yakkoindy8 ай бұрын
damn who knew that actually explaining the concept instead of just listing steps aimlessly would make me actually fucking learn this concept 😭😭😭 thank you
@dikdndkshxnd78644 ай бұрын
Thank you thank you sooooooooooooooo much you saved me from the exam
@AyushTomar-wp3is10 ай бұрын
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?
@alexmargrey4 ай бұрын
Thank you, proffesor
@kmjohnny10 ай бұрын
Quadratic solution now kinda makes sense geometrically - it's just a question if I want to add or remove from x square
@RoachRider66610 ай бұрын
Interesting analysis
@malforon489310 ай бұрын
Very helpful, thanks
@Areco77710 ай бұрын
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.
@youngmathematician915410 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!
@sensetivemasochist488727 күн бұрын
you are goated thank you
@adamdevmedia10 ай бұрын
I like to define perfect squares first and then you just use c=(b/2)^2 and see what's extra
@johanndohmann128110 ай бұрын
you are a genius!
@liamathew32603 ай бұрын
i finally know why it is in fact called "complete the square"
@erikhalvorseth39502 ай бұрын
Lovely. But I miss smth on the top line, the actual reasoning why our ancestors did this. Not only the left hand side of the original equation represent an area, but the right also. The geometric object with area X^2 + the geometric object with area 10*X equals the geometric object with area 24. Imagine you are an Egyptian geometer. To get algebraic solutions to area problems is his task.
@kavinesh_the_legend10 ай бұрын
And now I'm confused
@Momolaranya8 ай бұрын
im not confused any longer
@channelbuattv10 ай бұрын
why do we always assume that x is greater than the number?
@zemyaso10 ай бұрын
Graphs are not gonna be 100% accurate. If x was < or > or = the number, then just draw the x accordingly. This is just to get the idea of where completing the square comes from.
@channelbuattv10 ай бұрын
@@zemyaso When people draw (a±b)² sometimes they assume either a>b or a
@bprpmathbasics10 ай бұрын
It doesn’t matter. I could have done a smaller square first then a bigger one. 😃
@channelbuattv10 ай бұрын
@@bprpmathbasics Divide by 2 or multiply by ½?
@APUS_NUNN10 ай бұрын
... Und jetzt noch den Zusammenhang zwischen x=2 und der Abbildung... bzw x=-12 und der Abbildung 😮.....