b^2+6b=2

Solution for b^2+6b=2 equation:

Simplifying
b2 + 6b = 2

Reorder the terms:
6b + b2 = 2

Solving
6b + b2 = 2

Solving for variable 'b'.

Reorder the terms:
-2 + 6b + b2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 6b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 6b + 2 + b2 = 0 + 2

Reorder the terms:
-2 + 2 + 6b + b2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 6b + b2 = 0 + 2
6b + b2 = 0 + 2

Combine like terms: 0 + 2 = 2
6b + b2 = 2

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 = 2 + 9

Reorder the terms:
9 + 6b + b2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + 6b + b2 = 11

Factor a perfect square on the left side:
(b + 3)(b + 3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(b + 3) equal to 3.31662479 and -3.31662479.

Subproblem 1
b + 3 = 3.31662479

Simplifying
b + 3 = 3.31662479

Reorder the terms:
3 + b = 3.31662479

Solving
3 + b = 3.31662479

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 = 3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + b = 3.31662479 + -3
b = 3.31662479 + -3

Combine like terms: 3.31662479 + -3 = 0.31662479
b = 0.31662479

Simplifying
b = 0.31662479

Subproblem 2
b + 3 = -3.31662479

Simplifying
b + 3 = -3.31662479

Reorder the terms:
3 + b = -3.31662479

Solving
3 + b = -3.31662479

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 = -3.31662479 + -3

Combine like terms: 3 + -3 = 0
0 + b = -3.31662479 + -3
b = -3.31662479 + -3

Combine like terms: -3.31662479 + -3 = -6.31662479
b = -6.31662479

Simplifying
b = -6.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.31662479, -6.31662479}