2x^2+32=-16x2x2+32=−16x <- This is your equation
We will add 16x16x to both sides.
That will become
2x^2+32color(blue)+color(blue)16color(blue)x=-16xcolor(blue)+color(blue)16color(blue)x2x2+32+16x=−16x+16x
Now simplify it to become
2x^2+32+16x=02x2+32+16x=0
Now we will solve this quadratic equation by factoring.
2x^2+32+16x2x2+32+16x
= 2(x^2+8x+16)=2(x2+8x+16)
------->x^2+8x+16x2+8x+16
Then, we break this equations into groups.
x^2+8x+16 = (x^2+4x)+(4x+16)x2+8x+16=(x2+4x)+(4x+16) (The 8x8x was separated 4x4x in each side)
Then we factor out xx from x^2+4xx2+4x and 44 from 4x+164x+16.
Which gives us x(x+4)+4(x+4)x(x+4)+4(x+4)
Then we factor out (x+4)(x+4) to give us (x+4)(x+4)(x+4)(x+4).
Which is 2(x+4)(x+4)2(x+4)(x+4) and is also 2(x+4)^22(x+4)2
So, 2(x+4^2)=02(x+42)=0
Now, x+4=0x+4=0.
Now we subtract 44 from both sides.
x+4color(blue)-color(blue)4=0color(blue)-color(blue)4x+4−4=0−4
Then we simplify to x=-4x=−4
So, the answer is -4−4.