2x^2+2x-230=0

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Solution for 2x^2+2x-230=0 equation: 


Simplifying
2x2 + 2x + -230 = 0

Reorder the terms:
-230 + 2x + 2x2 = 0

Solving
-230 + 2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-115 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-115 + x + x2)' equal to zero and attempt to solve:

Simplifying
-115 + x + x2 = 0

Solving
-115 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + x + 115 + x2 = 0 + 115

Reorder the terms:
-115 + 115 + x + x2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + x + x2 = 0 + 115
x + x2 = 0 + 115

Combine like terms: 0 + 115 = 115
x + x2 = 115

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 = 115 + 0.25

Reorder the terms:
0.25 + x + x2 = 115 + 0.25

Combine like terms: 115 + 0.25 = 115.25
0.25 + x + x2 = 115.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 115.25

Calculate the square root of the right side: 10.735455277

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.735455277 and -10.735455277.


Subproblem 1
x + 0.5 = 10.735455277

Simplifying
x + 0.5 = 10.735455277

Reorder the terms:
0.5 + x = 10.735455277

Solving
0.5 + x = 10.735455277

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 = 10.735455277 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 10.735455277 + -0.5
x = 10.735455277 + -0.5

Combine like terms: 10.735455277 + -0.5 = 10.235455277
x = 10.235455277

Simplifying
x = 10.235455277


Subproblem 2
x + 0.5 = -10.735455277

Simplifying
x + 0.5 = -10.735455277

Reorder the terms:
0.5 + x = -10.735455277

Solving
0.5 + x = -10.735455277

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 = -10.735455277 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -10.735455277 + -0.5
x = -10.735455277 + -0.5

Combine like terms: -10.735455277 + -0.5 = -11.235455277
x = -11.235455277

Simplifying
x = -11.235455277


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.235455277, -11.235455277}
Solution
x = {10.235455277, -11.235455277}

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