b^2-10b-6=0

Solution for b^2-10b-6=0 equation:

Simplifying
b2 + -10b + -6 = 0

Reorder the terms:
-6 + -10b + b2 = 0

Solving
-6 + -10b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -10b + 6 + b2 = 0 + 6

Reorder the terms:
-6 + 6 + -10b + b2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -10b + b2 = 0 + 6
-10b + b2 = 0 + 6

Combine like terms: 0 + 6 = 6
-10b + b2 = 6

The b term is -10b.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10b + 25 + b2 = 6 + 25

Reorder the terms:
25 + -10b + b2 = 6 + 25

Combine like terms: 6 + 25 = 31
25 + -10b + b2 = 31

Factor a perfect square on the left side:
(b + -5)(b + -5) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(b + -5) equal to 5.567764363 and -5.567764363.

Subproblem 1
b + -5 = 5.567764363

Simplifying
b + -5 = 5.567764363

Reorder the terms:
-5 + b = 5.567764363

Solving
-5 + b = 5.567764363

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = 5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + b = 5.567764363 + 5
b = 5.567764363 + 5

Combine like terms: 5.567764363 + 5 = 10.567764363
b = 10.567764363

Simplifying
b = 10.567764363

Subproblem 2
b + -5 = -5.567764363

Simplifying
b + -5 = -5.567764363

Reorder the terms:
-5 + b = -5.567764363

Solving
-5 + b = -5.567764363

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = -5.567764363 + 5

Combine like terms: -5 + 5 = 0
0 + b = -5.567764363 + 5
b = -5.567764363 + 5

Combine like terms: -5.567764363 + 5 = -0.567764363
b = -0.567764363

Simplifying
b = -0.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {10.567764363, -0.567764363}