9b^2+18b-56=0

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Solution for 9b^2+18b-56=0 equation: 


Simplifying
9b2 + 18b + -56 = 0

Reorder the terms:
-56 + 18b + 9b2 = 0

Solving
-56 + 18b + 9b2 = 0

Solving for variable 'b'.

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

Divide each side by '9'.
-6.222222222 + 2b + b2 = 0

Move the constant term to the right:

Add '6.222222222' to each side of the equation.
-6.222222222 + 2b + 6.222222222 + b2 = 0 + 6.222222222

Reorder the terms:
-6.222222222 + 6.222222222 + 2b + b2 = 0 + 6.222222222

Combine like terms: -6.222222222 + 6.222222222 = 0.000000000
0.000000000 + 2b + b2 = 0 + 6.222222222
2b + b2 = 0 + 6.222222222

Combine like terms: 0 + 6.222222222 = 6.222222222
2b + b2 = 6.222222222

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 = 6.222222222 + 1

Reorder the terms:
1 + 2b + b2 = 6.222222222 + 1

Combine like terms: 6.222222222 + 1 = 7.222222222
1 + 2b + b2 = 7.222222222

Factor a perfect square on the left side:
(b + 1)(b + 1) = 7.222222222

Calculate the square root of the right side: 2.687419249

Break this problem into two subproblems by setting 
(b + 1) equal to 2.687419249 and -2.687419249.


Subproblem 1
b + 1 = 2.687419249

Simplifying
b + 1 = 2.687419249

Reorder the terms:
1 + b = 2.687419249

Solving
1 + b = 2.687419249

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 = 2.687419249 + -1

Combine like terms: 1 + -1 = 0
0 + b = 2.687419249 + -1
b = 2.687419249 + -1

Combine like terms: 2.687419249 + -1 = 1.687419249
b = 1.687419249

Simplifying
b = 1.687419249


Subproblem 2
b + 1 = -2.687419249

Simplifying
b + 1 = -2.687419249

Reorder the terms:
1 + b = -2.687419249

Solving
1 + b = -2.687419249

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 = -2.687419249 + -1

Combine like terms: 1 + -1 = 0
0 + b = -2.687419249 + -1
b = -2.687419249 + -1

Combine like terms: -2.687419249 + -1 = -3.687419249
b = -3.687419249

Simplifying
b = -3.687419249


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.687419249, -3.687419249}

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