-x^2-32x+256=0

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Solution for -x^2-32x+256=0 equation: 


Simplifying
-1x2 + -32x + 256 = 0

Reorder the terms:
256 + -32x + -1x2 = 0

Solving
256 + -32x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-256 + 32x + x2 = 0

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + 32x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + 32x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 32x + x2 = 0 + 256
32x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
32x + x2 = 256

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = 256 + 256

Reorder the terms:
256 + 32x + x2 = 256 + 256

Combine like terms: 256 + 256 = 512
256 + 32x + x2 = 512

Factor a perfect square on the left side:
(x + 16)(x + 16) = 512

Calculate the square root of the right side: 22.627416998

Break this problem into two subproblems by setting 
(x + 16) equal to 22.627416998 and -22.627416998.


Subproblem 1
x + 16 = 22.627416998

Simplifying
x + 16 = 22.627416998

Reorder the terms:
16 + x = 22.627416998

Solving
16 + x = 22.627416998

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + x = 22.627416998 + -16

Combine like terms: 16 + -16 = 0
0 + x = 22.627416998 + -16
x = 22.627416998 + -16

Combine like terms: 22.627416998 + -16 = 6.627416998
x = 6.627416998

Simplifying
x = 6.627416998


Subproblem 2
x + 16 = -22.627416998

Simplifying
x + 16 = -22.627416998

Reorder the terms:
16 + x = -22.627416998

Solving
16 + x = -22.627416998

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + x = -22.627416998 + -16

Combine like terms: 16 + -16 = 0
0 + x = -22.627416998 + -16
x = -22.627416998 + -16

Combine like terms: -22.627416998 + -16 = -38.627416998
x = -38.627416998

Simplifying
x = -38.627416998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.627416998, -38.627416998}

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