2x^2+36x+132=0

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Solution for 2x^2+36x+132=0 equation: 


Simplifying
2x2 + 36x + 132 = 0

Reorder the terms:
132 + 36x + 2x2 = 0

Solving
132 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(66 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(66 + 18x + x2)' equal to zero and attempt to solve:

Simplifying
66 + 18x + x2 = 0

Solving
66 + 18x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-66' to each side of the equation.
66 + 18x + -66 + x2 = 0 + -66

Reorder the terms:
66 + -66 + 18x + x2 = 0 + -66

Combine like terms: 66 + -66 = 0
0 + 18x + x2 = 0 + -66
18x + x2 = 0 + -66

Combine like terms: 0 + -66 = -66
18x + x2 = -66

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -66 + 81

Reorder the terms:
81 + 18x + x2 = -66 + 81

Combine like terms: -66 + 81 = 15
81 + 18x + x2 = 15

Factor a perfect square on the left side:
(x + 9)(x + 9) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 9) equal to 3.872983346 and -3.872983346.


Subproblem 1
x + 9 = 3.872983346

Simplifying
x + 9 = 3.872983346

Reorder the terms:
9 + x = 3.872983346

Solving
9 + x = 3.872983346

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 3.872983346 + -9

Combine like terms: 9 + -9 = 0
0 + x = 3.872983346 + -9
x = 3.872983346 + -9

Combine like terms: 3.872983346 + -9 = -5.127016654
x = -5.127016654

Simplifying
x = -5.127016654


Subproblem 2
x + 9 = -3.872983346

Simplifying
x + 9 = -3.872983346

Reorder the terms:
9 + x = -3.872983346

Solving
9 + x = -3.872983346

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -3.872983346 + -9

Combine like terms: 9 + -9 = 0
0 + x = -3.872983346 + -9
x = -3.872983346 + -9

Combine like terms: -3.872983346 + -9 = -12.872983346
x = -12.872983346

Simplifying
x = -12.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.127016654, -12.872983346}
Solution
x = {-5.127016654, -12.872983346}

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