9m^2+111m+264=0

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Solution for 9m^2+111m+264=0 equation: 


Simplifying
9m2 + 111m + 264 = 0

Reorder the terms:
264 + 111m + 9m2 = 0

Solving
264 + 111m + 9m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3'.
3(88 + 37m + 3m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(88 + 37m + 3m2)' equal to zero and attempt to solve:

Simplifying
88 + 37m + 3m2 = 0

Solving
88 + 37m + 3m2 = 0

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

Divide each side by '3'.
29.33333333 + 12.33333333m + m2 = 0

Move the constant term to the right:

Add '-29.33333333' to each side of the equation.
29.33333333 + 12.33333333m + -29.33333333 + m2 = 0 + -29.33333333

Reorder the terms:
29.33333333 + -29.33333333 + 12.33333333m + m2 = 0 + -29.33333333

Combine like terms: 29.33333333 + -29.33333333 = 0.00000000
0.00000000 + 12.33333333m + m2 = 0 + -29.33333333
12.33333333m + m2 = 0 + -29.33333333

Combine like terms: 0 + -29.33333333 = -29.33333333
12.33333333m + m2 = -29.33333333

The m term is 12.33333333m.  Take half its coefficient (6.166666665).
Square it (38.02777776) and add it to both sides.

Add '38.02777776' to each side of the equation.
12.33333333m + 38.02777776 + m2 = -29.33333333 + 38.02777776

Reorder the terms:
38.02777776 + 12.33333333m + m2 = -29.33333333 + 38.02777776

Combine like terms: -29.33333333 + 38.02777776 = 8.69444443
38.02777776 + 12.33333333m + m2 = 8.69444443

Factor a perfect square on the left side:
(m + 6.166666665)(m + 6.166666665) = 8.69444443

Calculate the square root of the right side: 2.948634333

Break this problem into two subproblems by setting 
(m + 6.166666665) equal to 2.948634333 and -2.948634333.


Subproblem 1
m + 6.166666665 = 2.948634333

Simplifying
m + 6.166666665 = 2.948634333

Reorder the terms:
6.166666665 + m = 2.948634333

Solving
6.166666665 + m = 2.948634333

Solving for variable 'm'.

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

Add '-6.166666665' to each side of the equation.
6.166666665 + -6.166666665 + m = 2.948634333 + -6.166666665

Combine like terms: 6.166666665 + -6.166666665 = 0.000000000
0.000000000 + m = 2.948634333 + -6.166666665
m = 2.948634333 + -6.166666665

Combine like terms: 2.948634333 + -6.166666665 = -3.218032332
m = -3.218032332

Simplifying
m = -3.218032332


Subproblem 2
m + 6.166666665 = -2.948634333

Simplifying
m + 6.166666665 = -2.948634333

Reorder the terms:
6.166666665 + m = -2.948634333

Solving
6.166666665 + m = -2.948634333

Solving for variable 'm'.

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

Add '-6.166666665' to each side of the equation.
6.166666665 + -6.166666665 + m = -2.948634333 + -6.166666665

Combine like terms: 6.166666665 + -6.166666665 = 0.000000000
0.000000000 + m = -2.948634333 + -6.166666665
m = -2.948634333 + -6.166666665

Combine like terms: -2.948634333 + -6.166666665 = -9.115300998
m = -9.115300998

Simplifying
m = -9.115300998


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-3.218032332, -9.115300998}
Solution
m = {-3.218032332, -9.115300998}

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