3m^2-41m+84=0

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Solution for 3m^2-41m+84=0 equation: 


Simplifying
3m2 + -41m + 84 = 0

Reorder the terms:
84 + -41m + 3m2 = 0

Solving
84 + -41m + 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'.
28 + -13.66666667m + m2 = 0

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -13.66666667m + -28 + m2 = 0 + -28

Reorder the terms:
28 + -28 + -13.66666667m + m2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -13.66666667m + m2 = 0 + -28
-13.66666667m + m2 = 0 + -28

Combine like terms: 0 + -28 = -28
-13.66666667m + m2 = -28

The m term is -13.66666667m.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667m + 46.69444447 + m2 = -28 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667m + m2 = -28 + 46.69444447

Combine like terms: -28 + 46.69444447 = 18.69444447
46.69444447 + -13.66666667m + m2 = 18.69444447

Factor a perfect square on the left side:
(m + -6.833333335)(m + -6.833333335) = 18.69444447

Calculate the square root of the right side: 4.32370726

Break this problem into two subproblems by setting 
(m + -6.833333335) equal to 4.32370726 and -4.32370726.


Subproblem 1
m + -6.833333335 = 4.32370726

Simplifying
m + -6.833333335 = 4.32370726

Reorder the terms:
-6.833333335 + m = 4.32370726

Solving
-6.833333335 + m = 4.32370726

Solving for variable 'm'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + m = 4.32370726 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + m = 4.32370726 + 6.833333335
m = 4.32370726 + 6.833333335

Combine like terms: 4.32370726 + 6.833333335 = 11.157040595
m = 11.157040595

Simplifying
m = 11.157040595


Subproblem 2
m + -6.833333335 = -4.32370726

Simplifying
m + -6.833333335 = -4.32370726

Reorder the terms:
-6.833333335 + m = -4.32370726

Solving
-6.833333335 + m = -4.32370726

Solving for variable 'm'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + m = -4.32370726 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + m = -4.32370726 + 6.833333335
m = -4.32370726 + 6.833333335

Combine like terms: -4.32370726 + 6.833333335 = 2.509626075
m = 2.509626075

Simplifying
m = 2.509626075


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {11.157040595, 2.509626075}

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