0=x^2-8x-120

Solution for 0=x^2-8x-120 equation:

Simplifying
0 = x2 + -8x + -120

Reorder the terms:
0 = -120 + -8x + x2

Solving
0 = -120 + -8x + x2

Solving for variable 'x'.

Combine like terms: 0 + 120 = 120
120 + 8x + -1x2 = -120 + -8x + x2 + 120 + 8x + -1x2

Reorder the terms:
120 + 8x + -1x2 = -120 + 120 + -8x + 8x + x2 + -1x2

Combine like terms: -120 + 120 = 0
120 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
120 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
120 + 8x + -1x2 = 0 + x2 + -1x2
120 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
120 + 8x + -1x2 = 0

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

Divide each side by '-1'.
-120 + -8x + x2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -8x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -8x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -8x + x2 = 0 + 120
-8x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-8x + x2 = 120

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 = 120 + 16

Reorder the terms:
16 + -8x + x2 = 120 + 16

Combine like terms: 120 + 16 = 136
16 + -8x + x2 = 136

Factor a perfect square on the left side:
(x + -4)(x + -4) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + -4) equal to 11.66190379 and -11.66190379.

Subproblem 1
x + -4 = 11.66190379

Simplifying
x + -4 = 11.66190379

Reorder the terms:
-4 + x = 11.66190379

Solving
-4 + x = 11.66190379

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 = 11.66190379 + 4

Combine like terms: -4 + 4 = 0
0 + x = 11.66190379 + 4
x = 11.66190379 + 4

Combine like terms: 11.66190379 + 4 = 15.66190379
x = 15.66190379

Simplifying
x = 15.66190379

Subproblem 2
x + -4 = -11.66190379

Simplifying
x + -4 = -11.66190379

Reorder the terms:
-4 + x = -11.66190379

Solving
-4 + x = -11.66190379

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 = -11.66190379 + 4

Combine like terms: -4 + 4 = 0
0 + x = -11.66190379 + 4
x = -11.66190379 + 4

Combine like terms: -11.66190379 + 4 = -7.66190379
x = -7.66190379

Simplifying
x = -7.66190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.66190379, -7.66190379}