b^2+6b-4=0

Solution for b^2+6b-4=0 equation:

Simplifying
b2 + 6b + -4 = 0

Reorder the terms:
-4 + 6b + b2 = 0

Solving
-4 + 6b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6b + 4 + b2 = 0 + 4

Reorder the terms:
-4 + 4 + 6b + b2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6b + b2 = 0 + 4
6b + b2 = 0 + 4

Combine like terms: 0 + 4 = 4
6b + b2 = 4

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 = 4 + 9

Reorder the terms:
9 + 6b + b2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6b + b2 = 13

Factor a perfect square on the left side:
(b + 3)(b + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(b + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1
b + 3 = 3.605551275

Simplifying
b + 3 = 3.605551275

Reorder the terms:
3 + b = 3.605551275

Solving
3 + b = 3.605551275

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 = 3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + b = 3.605551275 + -3
b = 3.605551275 + -3

Combine like terms: 3.605551275 + -3 = 0.605551275
b = 0.605551275

Simplifying
b = 0.605551275

Subproblem 2
b + 3 = -3.605551275

Simplifying
b + 3 = -3.605551275

Reorder the terms:
3 + b = -3.605551275

Solving
3 + b = -3.605551275

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 = -3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + b = -3.605551275 + -3
b = -3.605551275 + -3

Combine like terms: -3.605551275 + -3 = -6.605551275
b = -6.605551275

Simplifying
b = -6.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.605551275, -6.605551275}