x^2+8x-64=0

Solution for x^2+8x-64=0 equation:

Simplifying
x2 + 8x + -64 = 0

Reorder the terms:
-64 + 8x + x2 = 0

Solving
-64 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 8x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 8x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 8x + x2 = 0 + 64
8x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
8x + x2 = 64

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 64 + 16

Reorder the terms:
16 + 8x + x2 = 64 + 16

Combine like terms: 64 + 16 = 80
16 + 8x + x2 = 80

Factor a perfect square on the left side:
(x + 4)(x + 4) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + 4) equal to 8.94427191 and -8.94427191.

Subproblem 1
x + 4 = 8.94427191

Simplifying
x + 4 = 8.94427191

Reorder the terms:
4 + x = 8.94427191

Solving
4 + x = 8.94427191

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 8.94427191 + -4

Combine like terms: 4 + -4 = 0
0 + x = 8.94427191 + -4
x = 8.94427191 + -4

Combine like terms: 8.94427191 + -4 = 4.94427191
x = 4.94427191

Simplifying
x = 4.94427191

Subproblem 2
x + 4 = -8.94427191

Simplifying
x + 4 = -8.94427191

Reorder the terms:
4 + x = -8.94427191

Solving
4 + x = -8.94427191

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -8.94427191 + -4

Combine like terms: 4 + -4 = 0
0 + x = -8.94427191 + -4
x = -8.94427191 + -4

Combine like terms: -8.94427191 + -4 = -12.94427191
x = -12.94427191

Simplifying
x = -12.94427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.94427191, -12.94427191}