b^2-2b-22=0

Solution for b^2-2b-22=0 equation:

Simplifying
b2 + -2b + -22 = 0

Reorder the terms:
-22 + -2b + b2 = 0

Solving
-22 + -2b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -2b + 22 + b2 = 0 + 22

Reorder the terms:
-22 + 22 + -2b + b2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -2b + b2 = 0 + 22
-2b + b2 = 0 + 22

Combine like terms: 0 + 22 = 22
-2b + b2 = 22

The b term is -2b.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2b + 1 + b2 = 22 + 1

Reorder the terms:
1 + -2b + b2 = 22 + 1

Combine like terms: 22 + 1 = 23
1 + -2b + b2 = 23

Factor a perfect square on the left side:
(b + -1)(b + -1) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(b + -1) equal to 4.795831523 and -4.795831523.

Subproblem 1
b + -1 = 4.795831523

Simplifying
b + -1 = 4.795831523

Reorder the terms:
-1 + b = 4.795831523

Solving
-1 + b = 4.795831523

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = 4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + b = 4.795831523 + 1
b = 4.795831523 + 1

Combine like terms: 4.795831523 + 1 = 5.795831523
b = 5.795831523

Simplifying
b = 5.795831523

Subproblem 2
b + -1 = -4.795831523

Simplifying
b + -1 = -4.795831523

Reorder the terms:
-1 + b = -4.795831523

Solving
-1 + b = -4.795831523

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + b = -4.795831523 + 1

Combine like terms: -1 + 1 = 0
0 + b = -4.795831523 + 1
b = -4.795831523 + 1

Combine like terms: -4.795831523 + 1 = -3.795831523
b = -3.795831523

Simplifying
b = -3.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {5.795831523, -3.795831523}