2x^2+2x-156=0

Solution for 2x^2+2x-156=0 equation:

Simplifying
2x2 + 2x + -156 = 0

Reorder the terms:
-156 + 2x + 2x2 = 0

Solving
-156 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-78 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-78 + x + x2)' equal to zero and attempt to solve:

Simplifying
-78 + x + x2 = 0

Solving
-78 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + x + x2 = 0 + 78
x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
x + x2 = 78

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 = 78 + 0.25

Reorder the terms:
0.25 + x + x2 = 78 + 0.25

Combine like terms: 78 + 0.25 = 78.25
0.25 + x + x2 = 78.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.845903006 and -8.845903006.

Subproblem 1
x + 0.5 = 8.845903006

Simplifying
x + 0.5 = 8.845903006

Reorder the terms:
0.5 + x = 8.845903006

Solving
0.5 + x = 8.845903006

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 = 8.845903006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 8.845903006 + -0.5
x = 8.845903006 + -0.5

Combine like terms: 8.845903006 + -0.5 = 8.345903006
x = 8.345903006

Simplifying
x = 8.345903006

Subproblem 2
x + 0.5 = -8.845903006

Simplifying
x + 0.5 = -8.845903006

Reorder the terms:
0.5 + x = -8.845903006

Solving
0.5 + x = -8.845903006

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 = -8.845903006 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -8.845903006 + -0.5
x = -8.845903006 + -0.5

Combine like terms: -8.845903006 + -0.5 = -9.345903006
x = -9.345903006

Simplifying
x = -9.345903006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.345903006, -9.345903006}
Solution
x = {8.345903006, -9.345903006}