3b^2+25b-45=0

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Solution for 3b^2+25b-45=0 equation: 


Simplifying
3b2 + 25b + -45 = 0

Reorder the terms:
-45 + 25b + 3b2 = 0

Solving
-45 + 25b + 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 + 8.333333333b + b2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8.333333333b + 15 + b2 = 0 + 15

Reorder the terms:
-15 + 15 + 8.333333333b + b2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8.333333333b + b2 = 0 + 15
8.333333333b + b2 = 0 + 15

Combine like terms: 0 + 15 = 15
8.333333333b + b2 = 15

The b term is 8.333333333b.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333b + 17.36111111 + b2 = 15 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333b + b2 = 15 + 17.36111111

Combine like terms: 15 + 17.36111111 = 32.36111111
17.36111111 + 8.333333333b + b2 = 32.36111111

Factor a perfect square on the left side:
(b + 4.166666667)(b + 4.166666667) = 32.36111111

Calculate the square root of the right side: 5.688682722

Break this problem into two subproblems by setting 
(b + 4.166666667) equal to 5.688682722 and -5.688682722.


Subproblem 1
b + 4.166666667 = 5.688682722

Simplifying
b + 4.166666667 = 5.688682722

Reorder the terms:
4.166666667 + b = 5.688682722

Solving
4.166666667 + b = 5.688682722

Solving for variable 'b'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + b = 5.688682722 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + b = 5.688682722 + -4.166666667
b = 5.688682722 + -4.166666667

Combine like terms: 5.688682722 + -4.166666667 = 1.522016055
b = 1.522016055

Simplifying
b = 1.522016055


Subproblem 2
b + 4.166666667 = -5.688682722

Simplifying
b + 4.166666667 = -5.688682722

Reorder the terms:
4.166666667 + b = -5.688682722

Solving
4.166666667 + b = -5.688682722

Solving for variable 'b'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + b = -5.688682722 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + b = -5.688682722 + -4.166666667
b = -5.688682722 + -4.166666667

Combine like terms: -5.688682722 + -4.166666667 = -9.855349389
b = -9.855349389

Simplifying
b = -9.855349389


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.522016055, -9.855349389}

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