3m^2+5m-164=0

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Solution for 3m^2+5m-164=0 equation: 


Simplifying
3m2 + 5m + -164 = 0

Reorder the terms:
-164 + 5m + 3m2 = 0

Solving
-164 + 5m + 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'.
-54.66666667 + 1.666666667m + m2 = 0

Move the constant term to the right:

Add '54.66666667' to each side of the equation.
-54.66666667 + 1.666666667m + 54.66666667 + m2 = 0 + 54.66666667

Reorder the terms:
-54.66666667 + 54.66666667 + 1.666666667m + m2 = 0 + 54.66666667

Combine like terms: -54.66666667 + 54.66666667 = 0.00000000
0.00000000 + 1.666666667m + m2 = 0 + 54.66666667
1.666666667m + m2 = 0 + 54.66666667

Combine like terms: 0 + 54.66666667 = 54.66666667
1.666666667m + m2 = 54.66666667

The m term is 1.666666667m.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667m + 0.6944444447 + m2 = 54.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667m + m2 = 54.66666667 + 0.6944444447

Combine like terms: 54.66666667 + 0.6944444447 = 55.3611111147
0.6944444447 + 1.666666667m + m2 = 55.3611111147

Factor a perfect square on the left side:
(m + 0.8333333335)(m + 0.8333333335) = 55.3611111147

Calculate the square root of the right side: 7.440504762

Break this problem into two subproblems by setting 
(m + 0.8333333335) equal to 7.440504762 and -7.440504762.


Subproblem 1
m + 0.8333333335 = 7.440504762

Simplifying
m + 0.8333333335 = 7.440504762

Reorder the terms:
0.8333333335 + m = 7.440504762

Solving
0.8333333335 + m = 7.440504762

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = 7.440504762 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = 7.440504762 + -0.8333333335
m = 7.440504762 + -0.8333333335

Combine like terms: 7.440504762 + -0.8333333335 = 6.6071714285
m = 6.6071714285

Simplifying
m = 6.6071714285


Subproblem 2
m + 0.8333333335 = -7.440504762

Simplifying
m + 0.8333333335 = -7.440504762

Reorder the terms:
0.8333333335 + m = -7.440504762

Solving
0.8333333335 + m = -7.440504762

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = -7.440504762 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = -7.440504762 + -0.8333333335
m = -7.440504762 + -0.8333333335

Combine like terms: -7.440504762 + -0.8333333335 = -8.2738380955
m = -8.2738380955

Simplifying
m = -8.2738380955


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.6071714285, -8.2738380955}

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