9b^2+6b-11=0

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Solution for 9b^2+6b-11=0 equation: 


Simplifying
9b2 + 6b + -11 = 0

Reorder the terms:
-11 + 6b + 9b2 = 0

Solving
-11 + 6b + 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'.
-1.222222222 + 0.6666666667b + b2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + 0.6666666667b + 1.222222222 + b2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + 0.6666666667b + b2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + 0.6666666667b + b2 = 0 + 1.222222222
0.6666666667b + b2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
0.6666666667b + b2 = 1.222222222

The b term is 0.6666666667b.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667b + 0.1111111112 + b2 = 1.222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667b + b2 = 1.222222222 + 0.1111111112

Combine like terms: 1.222222222 + 0.1111111112 = 1.3333333332
0.1111111112 + 0.6666666667b + b2 = 1.3333333332

Factor a perfect square on the left side:
(b + 0.3333333334)(b + 0.3333333334) = 1.3333333332

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(b + 0.3333333334) equal to 1.154700538 and -1.154700538.


Subproblem 1
b + 0.3333333334 = 1.154700538

Simplifying
b + 0.3333333334 = 1.154700538

Reorder the terms:
0.3333333334 + b = 1.154700538

Solving
0.3333333334 + b = 1.154700538

Solving for variable 'b'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + b = 1.154700538 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + b = 1.154700538 + -0.3333333334
b = 1.154700538 + -0.3333333334

Combine like terms: 1.154700538 + -0.3333333334 = 0.8213672046
b = 0.8213672046

Simplifying
b = 0.8213672046


Subproblem 2
b + 0.3333333334 = -1.154700538

Simplifying
b + 0.3333333334 = -1.154700538

Reorder the terms:
0.3333333334 + b = -1.154700538

Solving
0.3333333334 + b = -1.154700538

Solving for variable 'b'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + b = -1.154700538 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + b = -1.154700538 + -0.3333333334
b = -1.154700538 + -0.3333333334

Combine like terms: -1.154700538 + -0.3333333334 = -1.4880338714
b = -1.4880338714

Simplifying
b = -1.4880338714


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.8213672046, -1.4880338714}

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