Question

What are the solutions of the quadratic equation?
2x^2 - 16x + 32 = 0

Will give fan and medal. Thank you in advance! :)

Answer 1

The solution is x = 4

Answer 2

Okay. Um, thank you, but could you tell me how? Like walk through with me how you got that answer? @Cardinal_Carlo

Answer 3

Do you know the quadratic formula?

Answer 4

No, sorry. @OrangeMaster

Answer 5

\[2(x ^{2} - 8x + 16) = 0\]
\[(x-4)^{2} = 0\]
\[x = 4\]

Answer 6

It is essential to answering the question. It is

x= -b +/- sqrt(b^2-4ac)/2a

Answer 7

The quadratic formula is too complicated and therefore impractical to use it in this particular case. But it is similarly effective.

Answer 8

\[x=\frac{ -b \pm \sqrt{b^{2}-4ac} }{ 2a }\]

Answer 9

Okay. How do you apply that to the equation though?

Answer 10

It's not needed?

Answer 11

2x^2 - 16x + 32 = 0

The 2 in front of x is 'a'
-16 is 'b'
32 is 'c'

Input the values and solve.

Answer 12

\[x=\frac{ -(-16) \pm \sqrt{-16^{2}-4(2)(32)}}{ 2(2) }\]

Answer 13

Here's a fun way
$$
(x - ?)^2+16 - ?^2=0\\
$$
To find that ? just take the coefficient of x, in this case 8 and divide it by 2
$$
(x - \cfrac{8}{2})^2+16 - \left (\cfrac{8}{2}\right )^2=0\\
$$

Just another approach.

Answer 14

-(-16)=16
-16^2=256
4*2*32=256
256-256=0
sqrt(0)=0
2*2=4
16/4=4

Answer 15

The plus/minus has no point when the sqrt of 4ac is 0

Answer 16

-3^2 + 16 - 4^2 = -9 ? @ybarrap

Answer 17

@ybarrap method works but it's confusing for starters

Answer 18

So, @Cardinal_Carlo is correct, but there's the explanation.

Answer 19

Or, an explanation rather.

Answer 20

Okay. Gotcha. Sorry guys, let me just read through what all of you said :) thank you very very much for helping me. I'm trying to understand. @OrangeMaster @Cardinal_Carlo @ybarrap

Answer 21

No problem, just try to use what is easiest for you to understand. :)

Answer 22

No x variables?
$$
-3^2 + 16 - 4^2 = -9
$$
If so
$$
-3^2 + 16 - 4^2 =-9+16-16=-9
$$
So the statement is true.

Answer 23

I think I'm starting to understand it a little. I see both of your methods and I feel a better about them :)

Answer 24

The quadratic formula may be hard to memorize and understand at first, but it will get the problem solved.

Answer 25

Okay. Thank you.

Answer 26

Thank you guys SO much! @OrangeMaster @Cardinal_Carlo @ybarrap

Answer 27

You're welcome
$$
\color{green}{\Huge {:-)}}
$$

Answer 28

You're welcome