x^2-32*2x-256=0

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

Simplifying
x2 + -32 * 2x + -256 = 0

Multiply -32 * 2
x2 + -64x + -256 = 0

Reorder the terms:
-256 + -64x + x2 = 0

Solving
-256 + -64x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + -64x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + -64x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + -64x + x2 = 0 + 256
-64x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
-64x + x2 = 256

The x term is -64x.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64x + 1024 + x2 = 256 + 1024

Reorder the terms:
1024 + -64x + x2 = 256 + 1024

Combine like terms: 256 + 1024 = 1280
1024 + -64x + x2 = 1280

Factor a perfect square on the left side:
(x + -32)(x + -32) = 1280

Calculate the square root of the right side: 35.77708764

Break this problem into two subproblems by setting 
(x + -32) equal to 35.77708764 and -35.77708764.

Subproblem 1
x + -32 = 35.77708764

Simplifying
x + -32 = 35.77708764

Reorder the terms:
-32 + x = 35.77708764

Solving
-32 + x = 35.77708764

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = 35.77708764 + 32

Combine like terms: -32 + 32 = 0
0 + x = 35.77708764 + 32
x = 35.77708764 + 32

Combine like terms: 35.77708764 + 32 = 67.77708764
x = 67.77708764

Simplifying
x = 67.77708764

Subproblem 2
x + -32 = -35.77708764

Simplifying
x + -32 = -35.77708764

Reorder the terms:
-32 + x = -35.77708764

Solving
-32 + x = -35.77708764

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = -35.77708764 + 32

Combine like terms: -32 + 32 = 0
0 + x = -35.77708764 + 32
x = -35.77708764 + 32

Combine like terms: -35.77708764 + 32 = -3.77708764
x = -3.77708764

Simplifying
x = -3.77708764

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {67.77708764, -3.77708764}