b^2-8b+9=0

Solution for b^2-8b+9=0 equation:

Simplifying
b2 + -8b + 9 = 0

Reorder the terms:
9 + -8b + b2 = 0

Solving
9 + -8b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8b + -9 + b2 = 0 + -9

Reorder the terms:
9 + -9 + -8b + b2 = 0 + -9

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

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

The b term is -8b.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8b + 16 + b2 = -9 + 16

Reorder the terms:
16 + -8b + b2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8b + b2 = 7

Factor a perfect square on the left side:
(b + -4)(b + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(b + -4) equal to 2.645751311 and -2.645751311.

Subproblem 1
b + -4 = 2.645751311

Simplifying
b + -4 = 2.645751311

Reorder the terms:
-4 + b = 2.645751311

Solving
-4 + b = 2.645751311

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = 2.645751311 + 4

Combine like terms: -4 + 4 = 0
0 + b = 2.645751311 + 4
b = 2.645751311 + 4

Combine like terms: 2.645751311 + 4 = 6.645751311
b = 6.645751311

Simplifying
b = 6.645751311

Subproblem 2
b + -4 = -2.645751311

Simplifying
b + -4 = -2.645751311

Reorder the terms:
-4 + b = -2.645751311

Solving
-4 + b = -2.645751311

Solving for variable 'b'.

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

Add '4' to each side of the equation.
-4 + 4 + b = -2.645751311 + 4

Combine like terms: -4 + 4 = 0
0 + b = -2.645751311 + 4
b = -2.645751311 + 4

Combine like terms: -2.645751311 + 4 = 1.354248689
b = 1.354248689

Simplifying
b = 1.354248689

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {6.645751311, 1.354248689}