2x^2-4x-132=0

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Solution for 2x^2-4x-132=0 equation: 


Simplifying
2x2 + -4x + -132 = 0

Reorder the terms:
-132 + -4x + 2x2 = 0

Solving
-132 + -4x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-66 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-66 + -2x + x2 = 0

Solving
-66 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -2x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + -2x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -2x + x2 = 0 + 66
-2x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
-2x + x2 = 66

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 66 + 1

Reorder the terms:
1 + -2x + x2 = 66 + 1

Combine like terms: 66 + 1 = 67
1 + -2x + x2 = 67

Factor a perfect square on the left side:
(x + -1)(x + -1) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(x + -1) equal to 8.185352772 and -8.185352772.


Subproblem 1
x + -1 = 8.185352772

Simplifying
x + -1 = 8.185352772

Reorder the terms:
-1 + x = 8.185352772

Solving
-1 + x = 8.185352772

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 8.185352772 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.185352772 + 1
x = 8.185352772 + 1

Combine like terms: 8.185352772 + 1 = 9.185352772
x = 9.185352772

Simplifying
x = 9.185352772


Subproblem 2
x + -1 = -8.185352772

Simplifying
x + -1 = -8.185352772

Reorder the terms:
-1 + x = -8.185352772

Solving
-1 + x = -8.185352772

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -8.185352772 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.185352772 + 1
x = -8.185352772 + 1

Combine like terms: -8.185352772 + 1 = -7.185352772
x = -7.185352772

Simplifying
x = -7.185352772


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.185352772, -7.185352772}
Solution
x = {9.185352772, -7.185352772}

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