3m^2-3m-4=0

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Solution for 3m^2-3m-4=0 equation: 


Simplifying
3m2 + -3m + -4 = 0

Reorder the terms:
-4 + -3m + 3m2 = 0

Solving
-4 + -3m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
-1.333333333 + -1m + m2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1m + 1.333333333 + m2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1m + m2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1m + m2 = 0 + 1.333333333
-1m + m2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1m + m2 = 1.333333333

The m term is -1m.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1m + 0.25 + m2 = 1.333333333 + 0.25

Reorder the terms:
0.25 + -1m + m2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
0.25 + -1m + m2 = 1.583333333

Factor a perfect square on the left side:
(m + -0.5)(m + -0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(m + -0.5) equal to 1.258305739 and -1.258305739.


Subproblem 1
m + -0.5 = 1.258305739

Simplifying
m + -0.5 = 1.258305739

Reorder the terms:
-0.5 + m = 1.258305739

Solving
-0.5 + m = 1.258305739

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = 1.258305739 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = 1.258305739 + 0.5
m = 1.258305739 + 0.5

Combine like terms: 1.258305739 + 0.5 = 1.758305739
m = 1.758305739

Simplifying
m = 1.758305739


Subproblem 2
m + -0.5 = -1.258305739

Simplifying
m + -0.5 = -1.258305739

Reorder the terms:
-0.5 + m = -1.258305739

Solving
-0.5 + m = -1.258305739

Solving for variable 'm'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + m = -1.258305739 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + m = -1.258305739 + 0.5
m = -1.258305739 + 0.5

Combine like terms: -1.258305739 + 0.5 = -0.758305739
m = -0.758305739

Simplifying
m = -0.758305739


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.758305739, -0.758305739}

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