3m^2-m-3=0

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


Simplifying
3m2 + -1m + -3 = 0

Reorder the terms:
-3 + -1m + 3m2 = 0

Solving
-3 + -1m + 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 + -0.3333333333m + m2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.3333333333m + 1 + m2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.3333333333m + m2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.3333333333m + m2 = 0 + 1
-0.3333333333m + m2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.3333333333m + m2 = 1

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 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333m + m2 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + -0.3333333333m + m2 = 1.02777777779

Factor a perfect square on the left side:
(m + -0.1666666667)(m + -0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(m + -0.1666666667) equal to 1.013793755 and -1.013793755.


Subproblem 1
m + -0.1666666667 = 1.013793755

Simplifying
m + -0.1666666667 = 1.013793755

Reorder the terms:
-0.1666666667 + m = 1.013793755

Solving
-0.1666666667 + m = 1.013793755

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 = 1.013793755 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = 1.013793755 + 0.1666666667
m = 1.013793755 + 0.1666666667

Combine like terms: 1.013793755 + 0.1666666667 = 1.1804604217
m = 1.1804604217

Simplifying
m = 1.1804604217


Subproblem 2
m + -0.1666666667 = -1.013793755

Simplifying
m + -0.1666666667 = -1.013793755

Reorder the terms:
-0.1666666667 + m = -1.013793755

Solving
-0.1666666667 + m = -1.013793755

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 = -1.013793755 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + m = -1.013793755 + 0.1666666667
m = -1.013793755 + 0.1666666667

Combine like terms: -1.013793755 + 0.1666666667 = -0.8471270883
m = -0.8471270883

Simplifying
m = -0.8471270883


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.1804604217, -0.8471270883}

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