b^2+27b-180=0

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Solution for b^2+27b-180=0 equation: 


Simplifying
b2 + 27b + -180 = 0

Reorder the terms:
-180 + 27b + b2 = 0

Solving
-180 + 27b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 27b + 180 + b2 = 0 + 180

Reorder the terms:
-180 + 180 + 27b + b2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 27b + b2 = 0 + 180
27b + b2 = 0 + 180

Combine like terms: 0 + 180 = 180
27b + b2 = 180

The b term is 27b.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27b + 182.25 + b2 = 180 + 182.25

Reorder the terms:
182.25 + 27b + b2 = 180 + 182.25

Combine like terms: 180 + 182.25 = 362.25
182.25 + 27b + b2 = 362.25

Factor a perfect square on the left side:
(b + 13.5)(b + 13.5) = 362.25

Calculate the square root of the right side: 19.032866311

Break this problem into two subproblems by setting 
(b + 13.5) equal to 19.032866311 and -19.032866311.


Subproblem 1
b + 13.5 = 19.032866311

Simplifying
b + 13.5 = 19.032866311

Reorder the terms:
13.5 + b = 19.032866311

Solving
13.5 + b = 19.032866311

Solving for variable 'b'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + b = 19.032866311 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + b = 19.032866311 + -13.5
b = 19.032866311 + -13.5

Combine like terms: 19.032866311 + -13.5 = 5.532866311
b = 5.532866311

Simplifying
b = 5.532866311


Subproblem 2
b + 13.5 = -19.032866311

Simplifying
b + 13.5 = -19.032866311

Reorder the terms:
13.5 + b = -19.032866311

Solving
13.5 + b = -19.032866311

Solving for variable 'b'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + b = -19.032866311 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + b = -19.032866311 + -13.5
b = -19.032866311 + -13.5

Combine like terms: -19.032866311 + -13.5 = -32.532866311
b = -32.532866311

Simplifying
b = -32.532866311


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.532866311, -32.532866311}

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