2x^2+2x-636=0

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Solution for 2x^2+2x-636=0 equation: 


Simplifying
2x2 + 2x + -636 = 0

Reorder the terms:
-636 + 2x + 2x2 = 0

Solving
-636 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-318 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-318 + x + x2)' equal to zero and attempt to solve:

Simplifying
-318 + x + x2 = 0

Solving
-318 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '318' to each side of the equation.
-318 + x + 318 + x2 = 0 + 318

Reorder the terms:
-318 + 318 + x + x2 = 0 + 318

Combine like terms: -318 + 318 = 0
0 + x + x2 = 0 + 318
x + x2 = 0 + 318

Combine like terms: 0 + 318 = 318
x + x2 = 318

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 = 318 + 0.25

Reorder the terms:
0.25 + x + x2 = 318 + 0.25

Combine like terms: 318 + 0.25 = 318.25
0.25 + x + x2 = 318.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 318.25

Calculate the square root of the right side: 17.839562775

Break this problem into two subproblems by setting 
(x + 0.5) equal to 17.839562775 and -17.839562775.


Subproblem 1
x + 0.5 = 17.839562775

Simplifying
x + 0.5 = 17.839562775

Reorder the terms:
0.5 + x = 17.839562775

Solving
0.5 + x = 17.839562775

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 = 17.839562775 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 17.839562775 + -0.5
x = 17.839562775 + -0.5

Combine like terms: 17.839562775 + -0.5 = 17.339562775
x = 17.339562775

Simplifying
x = 17.339562775


Subproblem 2
x + 0.5 = -17.839562775

Simplifying
x + 0.5 = -17.839562775

Reorder the terms:
0.5 + x = -17.839562775

Solving
0.5 + x = -17.839562775

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 = -17.839562775 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -17.839562775 + -0.5
x = -17.839562775 + -0.5

Combine like terms: -17.839562775 + -0.5 = -18.339562775
x = -18.339562775

Simplifying
x = -18.339562775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.339562775, -18.339562775}
Solution
x = {17.339562775, -18.339562775}

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