x^2+8x-72=0

Solution for x^2+8x-72=0 equation:

Simplifying
x2 + 8x + -72 = 0

Reorder the terms:
-72 + 8x + x2 = 0

Solving
-72 + 8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 8x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + 8x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 8x + x2 = 0 + 72
8x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
8x + x2 = 72

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 = 72 + 16

Reorder the terms:
16 + 8x + x2 = 72 + 16

Combine like terms: 72 + 16 = 88
16 + 8x + x2 = 88

Factor a perfect square on the left side:
(x + 4)(x + 4) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + 4) equal to 9.38083152 and -9.38083152.

Subproblem 1
x + 4 = 9.38083152

Simplifying
x + 4 = 9.38083152

Reorder the terms:
4 + x = 9.38083152

Solving
4 + x = 9.38083152

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 = 9.38083152 + -4

Combine like terms: 4 + -4 = 0
0 + x = 9.38083152 + -4
x = 9.38083152 + -4

Combine like terms: 9.38083152 + -4 = 5.38083152
x = 5.38083152

Simplifying
x = 5.38083152

Subproblem 2
x + 4 = -9.38083152

Simplifying
x + 4 = -9.38083152

Reorder the terms:
4 + x = -9.38083152

Solving
4 + x = -9.38083152

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 = -9.38083152 + -4

Combine like terms: 4 + -4 = 0
0 + x = -9.38083152 + -4
x = -9.38083152 + -4

Combine like terms: -9.38083152 + -4 = -13.38083152
x = -13.38083152

Simplifying
x = -13.38083152

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.38083152, -13.38083152}