2m^2+8m+4+6m+6-28=0

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Solution for 2m^2+8m+4+6m+6-28=0 equation: 


Simplifying
2m2 + 8m + 4 + 6m + 6 + -28 = 0

Reorder the terms:
4 + 6 + -28 + 8m + 6m + 2m2 = 0

Combine like terms: 4 + 6 = 10
10 + -28 + 8m + 6m + 2m2 = 0

Combine like terms: 10 + -28 = -18
-18 + 8m + 6m + 2m2 = 0

Combine like terms: 8m + 6m = 14m
-18 + 14m + 2m2 = 0

Solving
-18 + 14m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 7m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 7m + m2)' equal to zero and attempt to solve:

Simplifying
-9 + 7m + m2 = 0

Solving
-9 + 7m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 7m + 9 + m2 = 0 + 9

Reorder the terms:
-9 + 9 + 7m + m2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 7m + m2 = 0 + 9
7m + m2 = 0 + 9

Combine like terms: 0 + 9 = 9
7m + m2 = 9

The m term is 7m.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7m + 12.25 + m2 = 9 + 12.25

Reorder the terms:
12.25 + 7m + m2 = 9 + 12.25

Combine like terms: 9 + 12.25 = 21.25
12.25 + 7m + m2 = 21.25

Factor a perfect square on the left side:
(m + 3.5)(m + 3.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(m + 3.5) equal to 4.609772229 and -4.609772229.


Subproblem 1
m + 3.5 = 4.609772229

Simplifying
m + 3.5 = 4.609772229

Reorder the terms:
3.5 + m = 4.609772229

Solving
3.5 + m = 4.609772229

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = 4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = 4.609772229 + -3.5
m = 4.609772229 + -3.5

Combine like terms: 4.609772229 + -3.5 = 1.109772229
m = 1.109772229

Simplifying
m = 1.109772229


Subproblem 2
m + 3.5 = -4.609772229

Simplifying
m + 3.5 = -4.609772229

Reorder the terms:
3.5 + m = -4.609772229

Solving
3.5 + m = -4.609772229

Solving for variable 'm'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + m = -4.609772229 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + m = -4.609772229 + -3.5
m = -4.609772229 + -3.5

Combine like terms: -4.609772229 + -3.5 = -8.109772229
m = -8.109772229

Simplifying
m = -8.109772229


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.109772229, -8.109772229}
Solution
m = {1.109772229, -8.109772229}

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