9m^2-3m-3=4

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Solution for 9m^2-3m-3=4 equation: 


Simplifying
9m2 + -3m + -3 = 4

Reorder the terms:
-3 + -3m + 9m2 = 4

Solving
-3 + -3m + 9m2 = 4

Solving for variable 'm'.

Reorder the terms:
-3 + -4 + -3m + 9m2 = 4 + -4

Combine like terms: -3 + -4 = -7
-7 + -3m + 9m2 = 4 + -4

Combine like terms: 4 + -4 = 0
-7 + -3m + 9m2 = 0

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

Divide each side by '9'.
-0.7777777778 + -0.3333333333m + m2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -0.3333333333m + 0.7777777778 + m2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -0.3333333333m + m2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -0.3333333333m + m2 = 0 + 0.7777777778
-0.3333333333m + m2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-0.3333333333m + m2 = 0.7777777778

The m term is -0.3333333333m.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333m + 0.02777777779 + m2 = 0.7777777778 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333m + m2 = 0.7777777778 + 0.02777777779

Combine like terms: 0.7777777778 + 0.02777777779 = 0.80555555559
0.02777777779 + -0.3333333333m + m2 = 0.80555555559

Factor a perfect square on the left side:
(m + -0.1666666667)(m + -0.1666666667) = 0.80555555559

Calculate the square root of the right side: 0.897527468

Break this problem into two subproblems by setting 
(m + -0.1666666667) equal to 0.897527468 and -0.897527468.


Subproblem 1
m + -0.1666666667 = 0.897527468

Simplifying
m + -0.1666666667 = 0.897527468

Reorder the terms:
-0.1666666667 + m = 0.897527468

Solving
-0.1666666667 + m = 0.897527468

Solving for variable 'm'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + m = 0.897527468 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = 0.897527468 + 0.1666666667
m = 0.897527468 + 0.1666666667

Combine like terms: 0.897527468 + 0.1666666667 = 1.0641941347
m = 1.0641941347

Simplifying
m = 1.0641941347


Subproblem 2
m + -0.1666666667 = -0.897527468

Simplifying
m + -0.1666666667 = -0.897527468

Reorder the terms:
-0.1666666667 + m = -0.897527468

Solving
-0.1666666667 + m = -0.897527468

Solving for variable 'm'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + m = -0.897527468 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = -0.897527468 + 0.1666666667
m = -0.897527468 + 0.1666666667

Combine like terms: -0.897527468 + 0.1666666667 = -0.7308608013
m = -0.7308608013

Simplifying
m = -0.7308608013


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.0641941347, -0.7308608013}

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