24m^2+94m+28=0

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Solution for 24m^2+94m+28=0 equation: 


Simplifying
24m2 + 94m + 28 = 0

Reorder the terms:
28 + 94m + 24m2 = 0

Solving
28 + 94m + 24m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 47m + 12m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 47m + 12m2)' equal to zero and attempt to solve:

Simplifying
14 + 47m + 12m2 = 0

Solving
14 + 47m + 12m2 = 0

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

Divide each side by '12'.
1.166666667 + 3.916666667m + m2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + 3.916666667m + -1.166666667 + m2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + 3.916666667m + m2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + 3.916666667m + m2 = 0 + -1.166666667
3.916666667m + m2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
3.916666667m + m2 = -1.166666667

The m term is 3.916666667m.  Take half its coefficient (1.958333334).
Square it (3.835069447) and add it to both sides.

Add '3.835069447' to each side of the equation.
3.916666667m + 3.835069447 + m2 = -1.166666667 + 3.835069447

Reorder the terms:
3.835069447 + 3.916666667m + m2 = -1.166666667 + 3.835069447

Combine like terms: -1.166666667 + 3.835069447 = 2.66840278
3.835069447 + 3.916666667m + m2 = 2.66840278

Factor a perfect square on the left side:
(m + 1.958333334)(m + 1.958333334) = 2.66840278

Calculate the square root of the right side: 1.633524649

Break this problem into two subproblems by setting 
(m + 1.958333334) equal to 1.633524649 and -1.633524649.


Subproblem 1
m + 1.958333334 = 1.633524649

Simplifying
m + 1.958333334 = 1.633524649

Reorder the terms:
1.958333334 + m = 1.633524649

Solving
1.958333334 + m = 1.633524649

Solving for variable 'm'.

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

Add '-1.958333334' to each side of the equation.
1.958333334 + -1.958333334 + m = 1.633524649 + -1.958333334

Combine like terms: 1.958333334 + -1.958333334 = 0.000000000
0.000000000 + m = 1.633524649 + -1.958333334
m = 1.633524649 + -1.958333334

Combine like terms: 1.633524649 + -1.958333334 = -0.324808685
m = -0.324808685

Simplifying
m = -0.324808685


Subproblem 2
m + 1.958333334 = -1.633524649

Simplifying
m + 1.958333334 = -1.633524649

Reorder the terms:
1.958333334 + m = -1.633524649

Solving
1.958333334 + m = -1.633524649

Solving for variable 'm'.

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

Add '-1.958333334' to each side of the equation.
1.958333334 + -1.958333334 + m = -1.633524649 + -1.958333334

Combine like terms: 1.958333334 + -1.958333334 = 0.000000000
0.000000000 + m = -1.633524649 + -1.958333334
m = -1.633524649 + -1.958333334

Combine like terms: -1.633524649 + -1.958333334 = -3.591857983
m = -3.591857983

Simplifying
m = -3.591857983


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.324808685, -3.591857983}
Solution
m = {-0.324808685, -3.591857983}

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