3b^2+26b+45=0

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Solution for 3b^2+26b+45=0 equation: 


Simplifying
3b2 + 26b + 45 = 0

Reorder the terms:
45 + 26b + 3b2 = 0

Solving
45 + 26b + 3b2 = 0

Solving for variable 'b'.

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

Divide each side by '3'.
15 + 8.666666667b + b2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 8.666666667b + -15 + b2 = 0 + -15

Reorder the terms:
15 + -15 + 8.666666667b + b2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8.666666667b + b2 = 0 + -15
8.666666667b + b2 = 0 + -15

Combine like terms: 0 + -15 = -15
8.666666667b + b2 = -15

The b term is 8.666666667b.  Take half its coefficient (4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
8.666666667b + 18.77777778 + b2 = -15 + 18.77777778

Reorder the terms:
18.77777778 + 8.666666667b + b2 = -15 + 18.77777778

Combine like terms: -15 + 18.77777778 = 3.77777778
18.77777778 + 8.666666667b + b2 = 3.77777778

Factor a perfect square on the left side:
(b + 4.333333334)(b + 4.333333334) = 3.77777778

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(b + 4.333333334) equal to 1.943650632 and -1.943650632.


Subproblem 1
b + 4.333333334 = 1.943650632

Simplifying
b + 4.333333334 = 1.943650632

Reorder the terms:
4.333333334 + b = 1.943650632

Solving
4.333333334 + b = 1.943650632

Solving for variable 'b'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + b = 1.943650632 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + b = 1.943650632 + -4.333333334
b = 1.943650632 + -4.333333334

Combine like terms: 1.943650632 + -4.333333334 = -2.389682702
b = -2.389682702

Simplifying
b = -2.389682702


Subproblem 2
b + 4.333333334 = -1.943650632

Simplifying
b + 4.333333334 = -1.943650632

Reorder the terms:
4.333333334 + b = -1.943650632

Solving
4.333333334 + b = -1.943650632

Solving for variable 'b'.

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

Add '-4.333333334' to each side of the equation.
4.333333334 + -4.333333334 + b = -1.943650632 + -4.333333334

Combine like terms: 4.333333334 + -4.333333334 = 0.000000000
0.000000000 + b = -1.943650632 + -4.333333334
b = -1.943650632 + -4.333333334

Combine like terms: -1.943650632 + -4.333333334 = -6.276983966
b = -6.276983966

Simplifying
b = -6.276983966


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-2.389682702, -6.276983966}

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