2b^2+2b-132=0

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Solution for 2b^2+2b-132=0 equation: 


Simplifying
2b2 + 2b + -132 = 0

Reorder the terms:
-132 + 2b + 2b2 = 0

Solving
-132 + 2b + 2b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + b + b2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-66 + b + b2)' equal to zero and attempt to solve:

Simplifying
-66 + b + b2 = 0

Solving
-66 + b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + b + 66 + b2 = 0 + 66

Reorder the terms:
-66 + 66 + b + b2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + b + b2 = 0 + 66
b + b2 = 0 + 66

Combine like terms: 0 + 66 = 66
b + b2 = 66

The b term is b.  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.
b + 0.25 + b2 = 66 + 0.25

Reorder the terms:
0.25 + b + b2 = 66 + 0.25

Combine like terms: 66 + 0.25 = 66.25
0.25 + b + b2 = 66.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(b + 0.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
b + 0.5 = 8.139410298

Simplifying
b + 0.5 = 8.139410298

Reorder the terms:
0.5 + b = 8.139410298

Solving
0.5 + b = 8.139410298

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = 8.139410298 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 8.139410298 + -0.5
b = 8.139410298 + -0.5

Combine like terms: 8.139410298 + -0.5 = 7.639410298
b = 7.639410298

Simplifying
b = 7.639410298


Subproblem 2
b + 0.5 = -8.139410298

Simplifying
b + 0.5 = -8.139410298

Reorder the terms:
0.5 + b = -8.139410298

Solving
0.5 + b = -8.139410298

Solving for variable 'b'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + b = -8.139410298 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -8.139410298 + -0.5
b = -8.139410298 + -0.5

Combine like terms: -8.139410298 + -0.5 = -8.639410298
b = -8.639410298

Simplifying
b = -8.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {7.639410298, -8.639410298}
Solution
b = {7.639410298, -8.639410298}

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