Watch me solve this ALGEBRA equation!

Рет қаралды 11,483

Күн бұрын

Пікірлер: 70

@DhruvNobody Ай бұрын

Sir , This video was not a learning source for me but I do appreciate your efforts for making me use my brain , we need more teachers like you thank you for the efforts , 🍻 to the future generation

@juliamarple3785 Ай бұрын

I'm old, but as soon as that equation scrolled by, I knew that there was something special about it. And then I remembered! I still ♡ math!

@rocky7522 Ай бұрын

I come up with x=4, because 4 times 4 equals 16, 16 plus 4 equals 20, and 20 minus 20 equals 0.

@juergenilse3259 Ай бұрын

You may divide the left side by (x-4) (if x=4 is a soution) and end up with a tter, that direct shows the other soution (in this case (x^2+x20/(x-4)=(x+5)=(x-(-5)))) so x=-5 is the other solution.

@deaddocreallydeaddoc5244 Ай бұрын

I also did this in my head before he began and once again had to wonder why all the complexity. This is why I did so poorly in Algebra in HS (I'm 72, no calculators, etc.), but I could do general math in my head really well. Now, I realize that the purpose of math is to master complex system applications. You have to know all the definitions and rules. It's another language that one has to learn before doing it. A good algebra teacher knows how to draw you in step by step, which doesn't always happen.

@jeanlemire2681 Ай бұрын

I rewrite the equation as x^2 + x = 20. I immediately see that x = 4 is a solution since 4^2 + 4 = 20. Then, since it is the equation of a parabolic curve, and the discriminant (b^2 - 4 * a * c is positive, there must be another real answer. A quick inspection reveals that -5 is another answer since -5^2 + (-5) also = 20.

@stevenjohnson1143 Ай бұрын

Factoring it gives us (x+5)(x-4)=0 set each factor=0 x+5=0 x-4=0 x= -5 x=4

@jameswaybright5263 Ай бұрын

Dialogue is lengthy, but needed in explaining mathematics. 😊

@panlomito Ай бұрын

Without paper the answer was there in seconds: x1 = -5 and x2 = +4 But let us first establish that this is a quadratic equation meaning it is a parabola with possible 2 , 1 or zero crossings with the x-axis, that is what this = 0 part of the equation means. There is a little formula to determine if there are 2, 1 or zero crossings with the x-axis and is called the DETERMINATOR... With the general formula being ax² + bx + c the determinator will be D = b² -4ac... If D is positive there are two crossings, with D = 0 there is one touching point (being the top of the parabola) and if D is negative there is no crossing with the x-axis. In this case D = (+1)² - 4 . (+1) . (-20) = 1 + 80 = 81 and that is positive so there are 2 crossings with the x-axis. Next stop is to find the top of the parabola... the x-coordinate of the top or xtop = - b / 2a = - (+1) / 2.(+1) = -1 / 2 = - 1/2 so the symmetry-axis of the parabola is just left of the y-axis. Finding the coordinates of the top is very easy now: ytop = f(xtop) = f(-1/2) = (-1/2)² + (-1/2) - 20 = 1/4 - 1/2 - 20 = - 20 1/4 so the top of the parabola is on ( -1/2 , -20 1/4 ) The crossings with the x-axis are symmetrical to xtop and the distance from xtop to the crossings is delta = SQR(D) / 2a... in this case delta = SQR ( 81) / 2.(+1) = 9 / 2 = 4½ Now we can calculate the x-coordinates of the y=0 crossings on both sides of xtop: x1 = xtop MINUS delta and x2 = xtop PLUS delta or x1 = - ½ MINUS 4½ = -5 and x2 = -½ PLUS 4½ = +4 With this result we have the 3 most important points of the parabola: (x1 , 0) (xtop , ytop) (x2 , 0 ) or ( -5, 0 ) ( -½ , -20¼ ) ( 4 , 0 )

@Aiko_san-g5u Ай бұрын

goofy ahh yap

@MrMousley Ай бұрын

If X^2 + X - 20 = 0 then X^2 + X = 20 and this is one of those occasions where the answer just jumps out at you X = 4 4^2 + 4 (4 x 4) + 4 16 + 4 = 20 X = - 5 - 5^2 + - 5 (-5 x -5) - 5 25 - 5 = 20 so now I'll watch your video to see how to actually do it.

@as3346 Ай бұрын

love this

@vincentrobinette1507 Ай бұрын

Instinctively, I chose -5. (-5)(-5)=+25; 25+(-5)=20. 20-20=0. I didn't think to let X=4. (4X4=16+4=20)

@martinemjt Ай бұрын

x=4, x squared plus x =20, 4 times 4 plus four minus 20 =0

@juergenilse3259 Ай бұрын

We have a quadratic equation of the form x^2+px+q=0. According to Vieta, in tthis case the sum of the 2 solutions is -p and the product of the 2 solutions is q. x1=4 and x2=-5 are the vaues, which fulfi thheses conditions: x1+x2=-1 and x1*x2=-20. So thhe 2 solutions of thhis equation are x1=4 and x2=-5. We can chec thhe solutions: 4^2+4=16+4=20 (-5)^2+(5)=25-5=20

@tuannguyenvan6818 Ай бұрын

X1+x2 = -p => x1 =-( x2+p) thay vào tích x1 . x2 = q -(x2+p)x2=q x2 .x2 + p.x2 = -q => Bài toán chưa được chứng minh triệt để 😂😂. Cách của bạn là sự gán ghép .Sai

@juergenilse3259 Ай бұрын

@@tuannguyenvan6818 in fact, it is the way shown in the video. You may call it "qualified guessing", but the way is not wrong.

@tuannguyenvan6818 Ай бұрын

@@juergenilse3259 yes

@bjorneriksson6480 Ай бұрын

that factoring trick was a huge leap, Impressive-yes, but very poorly and anachronistically explained

@terry_willis Ай бұрын

Have a nice weekend everybody. Next week we will be working on solving the following: 2 + 2 = what ?

@juergenilse3259 Ай бұрын

2+2=11 (if we use 3 as the base of the nuber system) ... 😁

@smallhelmonabigship3524 Ай бұрын

@@juergenilse3259 Awesome! 10 + 10 = 100

@tomtke7351 Ай бұрын

Complete the square -- x^2 + x - 20 = 0 x^2 + x = 20 x^2 + x + (1/2)^2 = 20 + (1/2)^2 (x + (1/2))^2 = 20 + (1/4) = 81/4 (x + (1/2))^2 = 81/4 (x + (1/2)) = +/- 9/2 x = (+/- 9/2) - (1/2) = (8/2) , (-10/2) = 4 , -5 verify x^2 + x - 20 =? 0 x = 4? 16 + 4 - 20 =? 0 0 =❤ 0✔️ x = - 5 25 - 5 - 20 =? 0 0 =❤ 0✔️

@chrisdissanayake6979 Ай бұрын

X^2+X-20 =0 (X+5)(X-4)=0 Either X+5=0 or X-4=0 If X+5=0, X=-5 If X-4=0, X=4 Answer: X = -5 or X = 4

@brb__bathroom Ай бұрын

my brain be screaming at me "start a fire in the kitchen, it's easier to deal with"

@sr2291 Ай бұрын

Did it my head using deduction. x^2 + x = 20 + 0. 4^2 = 16 + 4 = 20

@ajitandyokothakur7191 Ай бұрын

There is a second solution as well, which is x = - 5 because x^2 + x - 20 = 0 is (x-4)(x+5) = 0, or, x 4 or x= -5. Dr. Ajit Thakur (USA).

@sr2291 Ай бұрын

@@ajitandyokothakur7191 I realized that watching the video. Thanks.

@DroneLearner Ай бұрын

What paint program do you use?

@subasu478 Ай бұрын

4 and 5

@Wes-x9p Ай бұрын

took me 5 seconds without any paper of caculator.

@russelllomando8460 Ай бұрын

got it (x+5=0) AND (x-4=0) X= -5 AND 4 in my head in 3 seconds thanks for the fun

@mrsmiley631 Ай бұрын

Your so smart.

@russelllomando8460 Ай бұрын

@mrsmiley631 I just love math. I'm 72 and it keeps my mind young.

@mrsmiley631 Ай бұрын

@@russelllomando8460 I was just busting chops. I was half hoping you were a teenager I could troll with my intentional "your" misuse. Cheers!

@russelllomando8460 Ай бұрын

@@mrsmiley631 👌

@johnhudelson2652 Ай бұрын

@russelllomando8460 I'm also 72, and it took me 5 seconds to solve this problem in my head.

@randallgreen4084 Ай бұрын

x is -5 or 4. Thank you for these.

@imagseer Ай бұрын

-5 and positive 4 in my head, but I struggled to prove it

@jimmiewilkinson6404 Ай бұрын

I'm

@rob876 Ай бұрын

(x - 4)(x + 5) = 0 x = 4 or x = -5

@MyronLane-n3c Ай бұрын

answer is 4, why make this so confussing when it is so simple?

@dazartingstall6680 Ай бұрын

Because 4 isn't the only possible answer.

@juergenilse3259 Ай бұрын

You missed the second solution. A (real) quadratic equation has etither no real solution, a doublle root as real sollution or 2 different real sollutions.. 4 is not a double root of this equation, so there must be another real solution /which mmmay be found using the abbc formula or by dividing the left side of the equation by (x-4) (if the right side is 0) if x=4 is one solution,or by using the theorem of vieta or ...

@gavindeane3670 Ай бұрын

It's not quite that simple. You missed half the answer.

@kimngo5197 Ай бұрын

X=4or x=-5

@jessydsouza5291 Ай бұрын

X=-5 ×=4

@lj6079 Ай бұрын

I was great at algebra but none of this makes sense anymore ☹️

@daviddavis7555 Ай бұрын

X=4

@josephlaura7387 Ай бұрын

X=-5,x=4

@tuannguyenvan6818 Ай бұрын

Good 👍

@hexbinoban6170 Ай бұрын

X^2 + X - 20 = 0 X^2 + X = 20 X(X +1) = 20 ---> DEAD END TRY SOMETHING ELSE : (X - 4)(X + 5) = 0 -5 * 4 = -20 , -5 + 4 = -1,. [-4 * 5 = -20 , -4 + 5 = 1] (X - 4)(X + 5) = 0 one of the properties of multiplication: if one of the factor is zero then the product is zero (X - 4) = 0, (X + 5) = 0 X - 4 = 0 X = 4 ####. X + 5 = 0 X = -5 Ans : X = {4, -5}