9m^2-12m-59=0

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Solution for 9m^2-12m-59=0 equation: 


Simplifying
9m2 + -12m + -59 = 0

Reorder the terms:
-59 + -12m + 9m2 = 0

Solving
-59 + -12m + 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'.
-6.555555556 + -1.333333333m + m2 = 0

Move the constant term to the right:

Add '6.555555556' to each side of the equation.
-6.555555556 + -1.333333333m + 6.555555556 + m2 = 0 + 6.555555556

Reorder the terms:
-6.555555556 + 6.555555556 + -1.333333333m + m2 = 0 + 6.555555556

Combine like terms: -6.555555556 + 6.555555556 = 0.000000000
0.000000000 + -1.333333333m + m2 = 0 + 6.555555556
-1.333333333m + m2 = 0 + 6.555555556

Combine like terms: 0 + 6.555555556 = 6.555555556
-1.333333333m + m2 = 6.555555556

The m term is -1.333333333m.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333m + 0.4444444442 + m2 = 6.555555556 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333m + m2 = 6.555555556 + 0.4444444442

Combine like terms: 6.555555556 + 0.4444444442 = 7.0000000002
0.4444444442 + -1.333333333m + m2 = 7.0000000002

Factor a perfect square on the left side:
(m + -0.6666666665)(m + -0.6666666665) = 7.0000000002

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(m + -0.6666666665) equal to 2.645751311 and -2.645751311.


Subproblem 1
m + -0.6666666665 = 2.645751311

Simplifying
m + -0.6666666665 = 2.645751311

Reorder the terms:
-0.6666666665 + m = 2.645751311

Solving
-0.6666666665 + m = 2.645751311

Solving for variable 'm'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + m = 2.645751311 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + m = 2.645751311 + 0.6666666665
m = 2.645751311 + 0.6666666665

Combine like terms: 2.645751311 + 0.6666666665 = 3.3124179775
m = 3.3124179775

Simplifying
m = 3.3124179775


Subproblem 2
m + -0.6666666665 = -2.645751311

Simplifying
m + -0.6666666665 = -2.645751311

Reorder the terms:
-0.6666666665 + m = -2.645751311

Solving
-0.6666666665 + m = -2.645751311

Solving for variable 'm'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + m = -2.645751311 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + m = -2.645751311 + 0.6666666665
m = -2.645751311 + 0.6666666665

Combine like terms: -2.645751311 + 0.6666666665 = -1.9790846445
m = -1.9790846445

Simplifying
m = -1.9790846445


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.3124179775, -1.9790846445}

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