2x^2+2x-12=180

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Solution for 2x^2+2x-12=180 equation: 


Simplifying
2x2 + 2x + -12 = 180

Reorder the terms:
-12 + 2x + 2x2 = 180

Solving
-12 + 2x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-12 + -180 + 2x + 2x2 = 180 + -180

Combine like terms: -12 + -180 = -192
-192 + 2x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-192 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-96 + x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-96 + x + x2)' equal to zero and attempt to solve:

Simplifying
-96 + x + x2 = 0

Solving
-96 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + x + x2 = 0 + 96
x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
x + x2 = 96

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 = 96 + 0.25

Reorder the terms:
0.25 + x + x2 = 96 + 0.25

Combine like terms: 96 + 0.25 = 96.25
0.25 + x + x2 = 96.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.810708435 and -9.810708435.


Subproblem 1
x + 0.5 = 9.810708435

Simplifying
x + 0.5 = 9.810708435

Reorder the terms:
0.5 + x = 9.810708435

Solving
0.5 + x = 9.810708435

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 = 9.810708435 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.810708435 + -0.5
x = 9.810708435 + -0.5

Combine like terms: 9.810708435 + -0.5 = 9.310708435
x = 9.310708435

Simplifying
x = 9.310708435


Subproblem 2
x + 0.5 = -9.810708435

Simplifying
x + 0.5 = -9.810708435

Reorder the terms:
0.5 + x = -9.810708435

Solving
0.5 + x = -9.810708435

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 = -9.810708435 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.810708435 + -0.5
x = -9.810708435 + -0.5

Combine like terms: -9.810708435 + -0.5 = -10.310708435
x = -10.310708435

Simplifying
x = -10.310708435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.310708435, -10.310708435}
Solution
x = {9.310708435, -10.310708435}

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