2x^2+2x-266=0

Solution for 2x^2+2x-266=0 equation:

Simplifying
2x2 + 2x + -266 = 0

Reorder the terms:
-266 + 2x + 2x2 = 0

Solving
-266 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-133 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-133 + x + x2)' equal to zero and attempt to solve:

Simplifying
-133 + x + x2 = 0

Solving
-133 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '133' to each side of the equation.
-133 + x + 133 + x2 = 0 + 133

Reorder the terms:
-133 + 133 + x + x2 = 0 + 133

Combine like terms: -133 + 133 = 0
0 + x + x2 = 0 + 133
x + x2 = 0 + 133

Combine like terms: 0 + 133 = 133
x + x2 = 133

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 = 133 + 0.25

Reorder the terms:
0.25 + x + x2 = 133 + 0.25

Combine like terms: 133 + 0.25 = 133.25
0.25 + x + x2 = 133.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 133.25

Calculate the square root of the right side: 11.543396381

Break this problem into two subproblems by setting 
(x + 0.5) equal to 11.543396381 and -11.543396381.

Subproblem 1
x + 0.5 = 11.543396381

Simplifying
x + 0.5 = 11.543396381

Reorder the terms:
0.5 + x = 11.543396381

Solving
0.5 + x = 11.543396381

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 = 11.543396381 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 11.543396381 + -0.5
x = 11.543396381 + -0.5

Combine like terms: 11.543396381 + -0.5 = 11.043396381
x = 11.043396381

Simplifying
x = 11.043396381

Subproblem 2
x + 0.5 = -11.543396381

Simplifying
x + 0.5 = -11.543396381

Reorder the terms:
0.5 + x = -11.543396381

Solving
0.5 + x = -11.543396381

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 = -11.543396381 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -11.543396381 + -0.5
x = -11.543396381 + -0.5

Combine like terms: -11.543396381 + -0.5 = -12.043396381
x = -12.043396381

Simplifying
x = -12.043396381

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.043396381, -12.043396381}
Solution
x = {11.043396381, -12.043396381}