b^2+25.5b=52.5

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Solution for b^2+25.5b=52.5 equation: 


Simplifying
b2 + 25.5b = 52.5

Reorder the terms:
25.5b + b2 = 52.5

Solving
25.5b + b2 = 52.5

Solving for variable 'b'.

Reorder the terms:
-52.5 + 25.5b + b2 = 52.5 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
-52.5 + 25.5b + b2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '52.5' to each side of the equation.
-52.5 + 25.5b + 52.5 + b2 = 0.0 + 52.5

Reorder the terms:
-52.5 + 52.5 + 25.5b + b2 = 0.0 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + 25.5b + b2 = 0.0 + 52.5
25.5b + b2 = 0.0 + 52.5

Combine like terms: 0.0 + 52.5 = 52.5
25.5b + b2 = 52.5

The b term is 25.5b.  Take half its coefficient (12.75).
Square it (162.5625) and add it to both sides.

Add '162.5625' to each side of the equation.
25.5b + 162.5625 + b2 = 52.5 + 162.5625

Reorder the terms:
162.5625 + 25.5b + b2 = 52.5 + 162.5625

Combine like terms: 52.5 + 162.5625 = 215.0625
162.5625 + 25.5b + b2 = 215.0625

Factor a perfect square on the left side:
(b + 12.75)(b + 12.75) = 215.0625

Calculate the square root of the right side: 14.665009376

Break this problem into two subproblems by setting 
(b + 12.75) equal to 14.665009376 and -14.665009376.


Subproblem 1
b + 12.75 = 14.665009376

Simplifying
b + 12.75 = 14.665009376

Reorder the terms:
12.75 + b = 14.665009376

Solving
12.75 + b = 14.665009376

Solving for variable 'b'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + b = 14.665009376 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + b = 14.665009376 + -12.75
b = 14.665009376 + -12.75

Combine like terms: 14.665009376 + -12.75 = 1.915009376
b = 1.915009376

Simplifying
b = 1.915009376


Subproblem 2
b + 12.75 = -14.665009376

Simplifying
b + 12.75 = -14.665009376

Reorder the terms:
12.75 + b = -14.665009376

Solving
12.75 + b = -14.665009376

Solving for variable 'b'.

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

Add '-12.75' to each side of the equation.
12.75 + -12.75 + b = -14.665009376 + -12.75

Combine like terms: 12.75 + -12.75 = 0.00
0.00 + b = -14.665009376 + -12.75
b = -14.665009376 + -12.75

Combine like terms: -14.665009376 + -12.75 = -27.415009376
b = -27.415009376

Simplifying
b = -27.415009376


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.915009376, -27.415009376}

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