9b^2+18b-24=0

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Solution for 9b^2+18b-24=0 equation: 


Simplifying
9b2 + 18b + -24 = 0

Reorder the terms:
-24 + 18b + 9b2 = 0

Solving
-24 + 18b + 9b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 6b + 3b2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 6b + 3b2)' equal to zero and attempt to solve:

Simplifying
-8 + 6b + 3b2 = 0

Solving
-8 + 6b + 3b2 = 0

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

Divide each side by '3'.
-2.666666667 + 2b + b2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 2b + 2.666666667 + b2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 2b + b2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 2b + b2 = 0 + 2.666666667
2b + b2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
2b + b2 = 2.666666667

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 = 2.666666667 + 1

Reorder the terms:
1 + 2b + b2 = 2.666666667 + 1

Combine like terms: 2.666666667 + 1 = 3.666666667
1 + 2b + b2 = 3.666666667

Factor a perfect square on the left side:
(b + 1)(b + 1) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(b + 1) equal to 1.914854216 and -1.914854216.


Subproblem 1
b + 1 = 1.914854216

Simplifying
b + 1 = 1.914854216

Reorder the terms:
1 + b = 1.914854216

Solving
1 + b = 1.914854216

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 = 1.914854216 + -1

Combine like terms: 1 + -1 = 0
0 + b = 1.914854216 + -1
b = 1.914854216 + -1

Combine like terms: 1.914854216 + -1 = 0.914854216
b = 0.914854216

Simplifying
b = 0.914854216


Subproblem 2
b + 1 = -1.914854216

Simplifying
b + 1 = -1.914854216

Reorder the terms:
1 + b = -1.914854216

Solving
1 + b = -1.914854216

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 = -1.914854216 + -1

Combine like terms: 1 + -1 = 0
0 + b = -1.914854216 + -1
b = -1.914854216 + -1

Combine like terms: -1.914854216 + -1 = -2.914854216
b = -2.914854216

Simplifying
b = -2.914854216


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.914854216, -2.914854216}
Solution
b = {0.914854216, -2.914854216}

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