2x^2-2x-108=0

Solution for 2x^2-2x-108=0 equation:

Simplifying
2x2 + -2x + -108 = 0

Reorder the terms:
-108 + -2x + 2x2 = 0

Solving
-108 + -2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -1x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-54 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-54 + -1x + x2 = 0

Solving
-54 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -1x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -1x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -1x + x2 = 0 + 54
-1x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-1x + x2 = 54

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 54 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 54 + 0.25

Combine like terms: 54 + 0.25 = 54.25
0.25 + -1x + x2 = 54.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + -0.5) equal to 7.365459931 and -7.365459931.

Subproblem 1
x + -0.5 = 7.365459931

Simplifying
x + -0.5 = 7.365459931

Reorder the terms:
-0.5 + x = 7.365459931

Solving
-0.5 + x = 7.365459931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 7.365459931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 7.365459931 + 0.5
x = 7.365459931 + 0.5

Combine like terms: 7.365459931 + 0.5 = 7.865459931
x = 7.865459931

Simplifying
x = 7.865459931

Subproblem 2
x + -0.5 = -7.365459931

Simplifying
x + -0.5 = -7.365459931

Reorder the terms:
-0.5 + x = -7.365459931

Solving
-0.5 + x = -7.365459931

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -7.365459931 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -7.365459931 + 0.5
x = -7.365459931 + 0.5

Combine like terms: -7.365459931 + 0.5 = -6.865459931
x = -6.865459931

Simplifying
x = -6.865459931

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.865459931, -6.865459931}
Solution
x = {7.865459931, -6.865459931}