How do you solve 2x ^ { 2} + 32= - 16x?

1 Answer
Sep 15, 2017

-4

Explanation:

2x^2+32=-16x <- This is your equation
We will add 16x to both sides.
That will become
2x^2+32color(blue)+color(blue)16color(blue)x=-16xcolor(blue)+color(blue)16color(blue)x

Now simplify it to become
2x^2+32+16x=0
Now we will solve this quadratic equation by factoring.
2x^2+32+16x
= 2(x^2+8x+16)
------->x^2+8x+16
Then, we break this equations into groups.
x^2+8x+16 = (x^2+4x)+(4x+16) (The 8x was separated 4x in each side)

Then we factor out x from x^2+4x and 4 from 4x+16.
Which gives us x(x+4)+4(x+4)
Then we factor out (x+4) to give us (x+4)(x+4).
Which is 2(x+4)(x+4) and is also 2(x+4)^2
So, 2(x+4^2)=0
Now, x+4=0.
Now we subtract 4 from both sides.
x+4color(blue)-color(blue)4=0color(blue)-color(blue)4
Then we simplify to x=-4
So, the answer is -4.