b^2+2b-180=0

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


Simplifying
b2 + 2b + -180 = 0

Reorder the terms:
-180 + 2b + b2 = 0

Solving
-180 + 2b + 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 + 2b + 180 + b2 = 0 + 180

Reorder the terms:
-180 + 180 + 2b + b2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 2b + b2 = 0 + 180
2b + b2 = 0 + 180

Combine like terms: 0 + 180 = 180
2b + b2 = 180

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

Add '1' to each side of the equation.
2b + 1 + b2 = 180 + 1

Reorder the terms:
1 + 2b + b2 = 180 + 1

Combine like terms: 180 + 1 = 181
1 + 2b + b2 = 181

Factor a perfect square on the left side:
(b + 1)(b + 1) = 181

Calculate the square root of the right side: 13.453624047

Break this problem into two subproblems by setting 
(b + 1) equal to 13.453624047 and -13.453624047.

Subproblem 1

b + 1 = 13.453624047 Simplifying b + 1 = 13.453624047 Reorder the terms: 1 + b = 13.453624047 Solving 1 + b = 13.453624047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + b = 13.453624047 + -1 b = 13.453624047 + -1 Combine like terms: 13.453624047 + -1 = 12.453624047 b = 12.453624047 Simplifying b = 12.453624047

Subproblem 2

b + 1 = -13.453624047 Simplifying b + 1 = -13.453624047 Reorder the terms: 1 + b = -13.453624047 Solving 1 + b = -13.453624047 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -13.453624047 + -1 Combine like terms: 1 + -1 = 0 0 + b = -13.453624047 + -1 b = -13.453624047 + -1 Combine like terms: -13.453624047 + -1 = -14.453624047 b = -14.453624047 Simplifying b = -14.453624047

Solution

The solution to the problem is based on the solutions from the subproblems. b = {12.453624047, -14.453624047}

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