9m^2+120m+16=0

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Solution for 9m^2+120m+16=0 equation: 


Simplifying
9m2 + 120m + 16 = 0

Reorder the terms:
16 + 120m + 9m2 = 0

Solving
16 + 120m + 9m2 = 0

Solving for variable 'm'.

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

Divide each side by '9'.
1.777777778 + 13.33333333m + m2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + 13.33333333m + -1.777777778 + m2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + 13.33333333m + m2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + 13.33333333m + m2 = 0 + -1.777777778
13.33333333m + m2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
13.33333333m + m2 = -1.777777778

The m term is 13.33333333m.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333m + 44.44444442 + m2 = -1.777777778 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333m + m2 = -1.777777778 + 44.44444442

Combine like terms: -1.777777778 + 44.44444442 = 42.666666642
44.44444442 + 13.33333333m + m2 = 42.666666642

Factor a perfect square on the left side:
(m + 6.666666665)(m + 6.666666665) = 42.666666642

Calculate the square root of the right side: 6.531972646

Break this problem into two subproblems by setting 
(m + 6.666666665) equal to 6.531972646 and -6.531972646.


Subproblem 1
m + 6.666666665 = 6.531972646

Simplifying
m + 6.666666665 = 6.531972646

Reorder the terms:
6.666666665 + m = 6.531972646

Solving
6.666666665 + m = 6.531972646

Solving for variable 'm'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + m = 6.531972646 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + m = 6.531972646 + -6.666666665
m = 6.531972646 + -6.666666665

Combine like terms: 6.531972646 + -6.666666665 = -0.134694019
m = -0.134694019

Simplifying
m = -0.134694019


Subproblem 2
m + 6.666666665 = -6.531972646

Simplifying
m + 6.666666665 = -6.531972646

Reorder the terms:
6.666666665 + m = -6.531972646

Solving
6.666666665 + m = -6.531972646

Solving for variable 'm'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + m = -6.531972646 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + m = -6.531972646 + -6.666666665
m = -6.531972646 + -6.666666665

Combine like terms: -6.531972646 + -6.666666665 = -13.198639311
m = -13.198639311

Simplifying
m = -13.198639311


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.134694019, -13.198639311}

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