9b^2-18b-67=-4

Solution for 9b^2-18b-67=-4 equation:

Simplifying
9b2 + -18b + -67 = -4

Reorder the terms:
-67 + -18b + 9b2 = -4

Solving
-67 + -18b + 9b2 = -4

Solving for variable 'b'.

Reorder the terms:
-67 + 4 + -18b + 9b2 = -4 + 4

Combine like terms: -67 + 4 = -63
-63 + -18b + 9b2 = -4 + 4

Combine like terms: -4 + 4 = 0
-63 + -18b + 9b2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-7 + -2b + b2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-7 + -2b + b2)' equal to zero and attempt to solve:

Simplifying
-7 + -2b + b2 = 0

Solving
-7 + -2b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2b + 7 + b2 = 0 + 7

Reorder the terms:
-7 + 7 + -2b + b2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2b + b2 = 0 + 7
-2b + b2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2b + b2 = 7

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 = 7 + 1

Reorder the terms:
1 + -2b + b2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2b + b2 = 8

Factor a perfect square on the left side:
(b + -1)(b + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(b + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1
b + -1 = 2.828427125

Simplifying
b + -1 = 2.828427125

Reorder the terms:
-1 + b = 2.828427125

Solving
-1 + b = 2.828427125

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 = 2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + b = 2.828427125 + 1
b = 2.828427125 + 1

Combine like terms: 2.828427125 + 1 = 3.828427125
b = 3.828427125

Simplifying
b = 3.828427125

Subproblem 2
b + -1 = -2.828427125

Simplifying
b + -1 = -2.828427125

Reorder the terms:
-1 + b = -2.828427125

Solving
-1 + b = -2.828427125

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 = -2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + b = -2.828427125 + 1
b = -2.828427125 + 1

Combine like terms: -2.828427125 + 1 = -1.828427125
b = -1.828427125

Simplifying
b = -1.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.828427125, -1.828427125}
Solution
b = {3.828427125, -1.828427125}