2m^2+24m-16=0

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Solution for 2m^2+24m-16=0 equation: 


Simplifying
2m2 + 24m + -16 = 0

Reorder the terms:
-16 + 24m + 2m2 = 0

Solving
-16 + 24m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 12m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 12m + m2)' equal to zero and attempt to solve:

Simplifying
-8 + 12m + m2 = 0

Solving
-8 + 12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 12m + 8 + m2 = 0 + 8

Reorder the terms:
-8 + 8 + 12m + m2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 12m + m2 = 0 + 8
12m + m2 = 0 + 8

Combine like terms: 0 + 8 = 8
12m + m2 = 8

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 = 8 + 36

Reorder the terms:
36 + 12m + m2 = 8 + 36

Combine like terms: 8 + 36 = 44
36 + 12m + m2 = 44

Factor a perfect square on the left side:
(m + 6)(m + 6) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(m + 6) equal to 6.633249581 and -6.633249581.


Subproblem 1
m + 6 = 6.633249581

Simplifying
m + 6 = 6.633249581

Reorder the terms:
6 + m = 6.633249581

Solving
6 + m = 6.633249581

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 = 6.633249581 + -6

Combine like terms: 6 + -6 = 0
0 + m = 6.633249581 + -6
m = 6.633249581 + -6

Combine like terms: 6.633249581 + -6 = 0.633249581
m = 0.633249581

Simplifying
m = 0.633249581


Subproblem 2
m + 6 = -6.633249581

Simplifying
m + 6 = -6.633249581

Reorder the terms:
6 + m = -6.633249581

Solving
6 + m = -6.633249581

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 = -6.633249581 + -6

Combine like terms: 6 + -6 = 0
0 + m = -6.633249581 + -6
m = -6.633249581 + -6

Combine like terms: -6.633249581 + -6 = -12.633249581
m = -12.633249581

Simplifying
m = -12.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.633249581, -12.633249581}
Solution
m = {0.633249581, -12.633249581}

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