2x^2+2x-122=0

Solution for 2x^2+2x-122=0 equation:

Simplifying
2x2 + 2x + -122 = 0

Reorder the terms:
-122 + 2x + 2x2 = 0

Solving
-122 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-61 + x + x2)' equal to zero and attempt to solve:

Simplifying
-61 + x + x2 = 0

Solving
-61 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + x + x2 = 0 + 61
x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
x + x2 = 61

The x term is x.  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.
x + 0.25 + x2 = 61 + 0.25

Reorder the terms:
0.25 + x + x2 = 61 + 0.25

Combine like terms: 61 + 0.25 = 61.25
0.25 + x + x2 = 61.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 61.25

Calculate the square root of the right side: 7.826237921

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.826237921 and -7.826237921.

Subproblem 1
x + 0.5 = 7.826237921

Simplifying
x + 0.5 = 7.826237921

Reorder the terms:
0.5 + x = 7.826237921

Solving
0.5 + x = 7.826237921

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 = 7.826237921 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7.826237921 + -0.5
x = 7.826237921 + -0.5

Combine like terms: 7.826237921 + -0.5 = 7.326237921
x = 7.326237921

Simplifying
x = 7.326237921

Subproblem 2
x + 0.5 = -7.826237921

Simplifying
x + 0.5 = -7.826237921

Reorder the terms:
0.5 + x = -7.826237921

Solving
0.5 + x = -7.826237921

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 = -7.826237921 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7.826237921 + -0.5
x = -7.826237921 + -0.5

Combine like terms: -7.826237921 + -0.5 = -8.326237921
x = -8.326237921

Simplifying
x = -8.326237921

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.326237921, -8.326237921}
Solution
x = {7.326237921, -8.326237921}