0=2m^2+24m+36

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Solution for 0=2m^2+24m+36 equation: 


Simplifying
0 = 2m2 + 24m + 36

Reorder the terms:
0 = 36 + 24m + 2m2

Solving
0 = 36 + 24m + 2m2

Solving for variable 'm'.

Combine like terms: 0 + -36 = -36
-36 + -24m + -2m2 = 36 + 24m + 2m2 + -36 + -24m + -2m2

Reorder the terms:
-36 + -24m + -2m2 = 36 + -36 + 24m + -24m + 2m2 + -2m2

Combine like terms: 36 + -36 = 0
-36 + -24m + -2m2 = 0 + 24m + -24m + 2m2 + -2m2
-36 + -24m + -2m2 = 24m + -24m + 2m2 + -2m2

Combine like terms: 24m + -24m = 0
-36 + -24m + -2m2 = 0 + 2m2 + -2m2
-36 + -24m + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
-36 + -24m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(18 + 12m + m2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(18 + 12m + m2)' equal to zero and attempt to solve:

Simplifying
18 + 12m + m2 = 0

Solving
18 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 12m + -18 + m2 = 0 + -18

Reorder the terms:
18 + -18 + 12m + m2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 12m + m2 = 0 + -18
12m + m2 = 0 + -18

Combine like terms: 0 + -18 = -18
12m + m2 = -18

The m term is 12m.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12m + 36 + m2 = -18 + 36

Reorder the terms:
36 + 12m + m2 = -18 + 36

Combine like terms: -18 + 36 = 18
36 + 12m + m2 = 18

Factor a perfect square on the left side:
(m + 6)(m + 6) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(m + 6) equal to 4.242640687 and -4.242640687.


Subproblem 1
m + 6 = 4.242640687

Simplifying
m + 6 = 4.242640687

Reorder the terms:
6 + m = 4.242640687

Solving
6 + m = 4.242640687

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = 4.242640687 + -6

Combine like terms: 6 + -6 = 0
0 + m = 4.242640687 + -6
m = 4.242640687 + -6

Combine like terms: 4.242640687 + -6 = -1.757359313
m = -1.757359313

Simplifying
m = -1.757359313


Subproblem 2
m + 6 = -4.242640687

Simplifying
m + 6 = -4.242640687

Reorder the terms:
6 + m = -4.242640687

Solving
6 + m = -4.242640687

Solving for variable 'm'.

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

Add '-6' to each side of the equation.
6 + -6 + m = -4.242640687 + -6

Combine like terms: 6 + -6 = 0
0 + m = -4.242640687 + -6
m = -4.242640687 + -6

Combine like terms: -4.242640687 + -6 = -10.242640687
m = -10.242640687

Simplifying
m = -10.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.757359313, -10.242640687}
Solution
m = {-1.757359313, -10.242640687}

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