b^2-26b-135=0

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Solution for b^2-26b-135=0 equation: 


Simplifying
b2 + -26b + -135 = 0

Reorder the terms:
-135 + -26b + b2 = 0

Solving
-135 + -26b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + -26b + 135 + b2 = 0 + 135

Reorder the terms:
-135 + 135 + -26b + b2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + -26b + b2 = 0 + 135
-26b + b2 = 0 + 135

Combine like terms: 0 + 135 = 135
-26b + b2 = 135

The b term is -26b.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26b + 169 + b2 = 135 + 169

Reorder the terms:
169 + -26b + b2 = 135 + 169

Combine like terms: 135 + 169 = 304
169 + -26b + b2 = 304

Factor a perfect square on the left side:
(b + -13)(b + -13) = 304

Calculate the square root of the right side: 17.435595774

Break this problem into two subproblems by setting 
(b + -13) equal to 17.435595774 and -17.435595774.


Subproblem 1
b + -13 = 17.435595774

Simplifying
b + -13 = 17.435595774

Reorder the terms:
-13 + b = 17.435595774

Solving
-13 + b = 17.435595774

Solving for variable 'b'.

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

Add '13' to each side of the equation.
-13 + 13 + b = 17.435595774 + 13

Combine like terms: -13 + 13 = 0
0 + b = 17.435595774 + 13
b = 17.435595774 + 13

Combine like terms: 17.435595774 + 13 = 30.435595774
b = 30.435595774

Simplifying
b = 30.435595774


Subproblem 2
b + -13 = -17.435595774

Simplifying
b + -13 = -17.435595774

Reorder the terms:
-13 + b = -17.435595774

Solving
-13 + b = -17.435595774

Solving for variable 'b'.

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

Add '13' to each side of the equation.
-13 + 13 + b = -17.435595774 + 13

Combine like terms: -13 + 13 = 0
0 + b = -17.435595774 + 13
b = -17.435595774 + 13

Combine like terms: -17.435595774 + 13 = -4.435595774
b = -4.435595774

Simplifying
b = -4.435595774


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {30.435595774, -4.435595774}

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