b^2+6b-1=5

Solution for b^2+6b-1=5 equation:

Simplifying
b2 + 6b + -1 = 5

Reorder the terms:
-1 + 6b + b2 = 5

Solving
-1 + 6b + b2 = 5

Solving for variable 'b'.

Reorder the terms:
-1 + -5 + 6b + b2 = 5 + -5

Combine like terms: -1 + -5 = -6
-6 + 6b + b2 = 5 + -5

Combine like terms: 5 + -5 = 0
-6 + 6b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6b + 6 + b2 = 0 + 6

Reorder the terms:
-6 + 6 + 6b + b2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6b + b2 = 0 + 6
6b + b2 = 0 + 6

Combine like terms: 0 + 6 = 6
6b + b2 = 6

The b term is 6b.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6b + 9 + b2 = 6 + 9

Reorder the terms:
9 + 6b + b2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6b + b2 = 15

Factor a perfect square on the left side:
(b + 3)(b + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(b + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1
b + 3 = 3.872983346

Simplifying
b + 3 = 3.872983346

Reorder the terms:
3 + b = 3.872983346

Solving
3 + b = 3.872983346

Solving for variable 'b'.

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

Add '-3' to each side of the equation.
3 + -3 + b = 3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + b = 3.872983346 + -3
b = 3.872983346 + -3

Combine like terms: 3.872983346 + -3 = 0.872983346
b = 0.872983346

Simplifying
b = 0.872983346

Subproblem 2
b + 3 = -3.872983346

Simplifying
b + 3 = -3.872983346

Reorder the terms:
3 + b = -3.872983346

Solving
3 + b = -3.872983346

Solving for variable 'b'.

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

Add '-3' to each side of the equation.
3 + -3 + b = -3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + b = -3.872983346 + -3
b = -3.872983346 + -3

Combine like terms: -3.872983346 + -3 = -6.872983346
b = -6.872983346

Simplifying
b = -6.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.872983346, -6.872983346}