-2x^2-12x+132=0

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Solution for -2x^2-12x+132=0 equation: 


Simplifying
-2x2 + -12x + 132 = 0

Reorder the terms:
132 + -12x + -2x2 = 0

Solving
132 + -12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(66 + -6x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(66 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
66 + -6x + -1x2 = 0

Solving
66 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-66 + 6x + x2 = 0

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 6x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 6x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 6x + x2 = 0 + 66
6x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
6x + x2 = 66

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 66 + 9

Reorder the terms:
9 + 6x + x2 = 66 + 9

Combine like terms: 66 + 9 = 75
9 + 6x + x2 = 75

Factor a perfect square on the left side:
(x + 3)(x + 3) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 3) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 3 = 8.660254038

Simplifying
x + 3 = 8.660254038

Reorder the terms:
3 + x = 8.660254038

Solving
3 + x = 8.660254038

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 8.660254038 + -3

Combine like terms: 3 + -3 = 0
0 + x = 8.660254038 + -3
x = 8.660254038 + -3

Combine like terms: 8.660254038 + -3 = 5.660254038
x = 5.660254038

Simplifying
x = 5.660254038


Subproblem 2
x + 3 = -8.660254038

Simplifying
x + 3 = -8.660254038

Reorder the terms:
3 + x = -8.660254038

Solving
3 + x = -8.660254038

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = -8.660254038 + -3

Combine like terms: 3 + -3 = 0
0 + x = -8.660254038 + -3
x = -8.660254038 + -3

Combine like terms: -8.660254038 + -3 = -11.660254038
x = -11.660254038

Simplifying
x = -11.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.660254038, -11.660254038}
Solution
x = {5.660254038, -11.660254038}

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