9b^2-18b-41=8

Solution for 9b^2-18b-41=8 equation:

Simplifying
9b2 + -18b + -41 = 8

Reorder the terms:
-41 + -18b + 9b2 = 8

Solving
-41 + -18b + 9b2 = 8

Solving for variable 'b'.

Reorder the terms:
-41 + -8 + -18b + 9b2 = 8 + -8

Combine like terms: -41 + -8 = -49
-49 + -18b + 9b2 = 8 + -8

Combine like terms: 8 + -8 = 0
-49 + -18b + 9b2 = 0

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-5.444444444 + -2b + b2 = 0

Move the constant term to the right:

Add '5.444444444' to each side of the equation.
-5.444444444 + -2b + 5.444444444 + b2 = 0 + 5.444444444

Reorder the terms:
-5.444444444 + 5.444444444 + -2b + b2 = 0 + 5.444444444

Combine like terms: -5.444444444 + 5.444444444 = 0.000000000
0.000000000 + -2b + b2 = 0 + 5.444444444
-2b + b2 = 0 + 5.444444444

Combine like terms: 0 + 5.444444444 = 5.444444444
-2b + b2 = 5.444444444

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 = 5.444444444 + 1

Reorder the terms:
1 + -2b + b2 = 5.444444444 + 1

Combine like terms: 5.444444444 + 1 = 6.444444444
1 + -2b + b2 = 6.444444444

Factor a perfect square on the left side:
(b + -1)(b + -1) = 6.444444444

Calculate the square root of the right side: 2.538591035

Break this problem into two subproblems by setting 
(b + -1) equal to 2.538591035 and -2.538591035.

Subproblem 1
b + -1 = 2.538591035

Simplifying
b + -1 = 2.538591035

Reorder the terms:
-1 + b = 2.538591035

Solving
-1 + b = 2.538591035

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 = 2.538591035 + 1

Combine like terms: -1 + 1 = 0
0 + b = 2.538591035 + 1
b = 2.538591035 + 1

Combine like terms: 2.538591035 + 1 = 3.538591035
b = 3.538591035

Simplifying
b = 3.538591035

Subproblem 2
b + -1 = -2.538591035

Simplifying
b + -1 = -2.538591035

Reorder the terms:
-1 + b = -2.538591035

Solving
-1 + b = -2.538591035

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 = -2.538591035 + 1

Combine like terms: -1 + 1 = 0
0 + b = -2.538591035 + 1
b = -2.538591035 + 1

Combine like terms: -2.538591035 + 1 = -1.538591035
b = -1.538591035

Simplifying
b = -1.538591035

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.538591035, -1.538591035}