2m^2-24m+32=0

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Solution for 2m^2-24m+32=0 equation: 


Simplifying
2m2 + -24m + 32 = 0

Reorder the terms:
32 + -24m + 2m2 = 0

Solving
32 + -24m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -12m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -12m + m2)' equal to zero and attempt to solve:

Simplifying
16 + -12m + m2 = 0

Solving
16 + -12m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12m + -16 + m2 = 0 + -16

Reorder the terms:
16 + -16 + -12m + m2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12m + m2 = 0 + -16
-12m + m2 = 0 + -16

Combine like terms: 0 + -16 = -16
-12m + m2 = -16

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 = -16 + 36

Reorder the terms:
36 + -12m + m2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12m + m2 = 20

Factor a perfect square on the left side:
(m + -6)(m + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(m + -6) equal to 4.472135955 and -4.472135955.


Subproblem 1
m + -6 = 4.472135955

Simplifying
m + -6 = 4.472135955

Reorder the terms:
-6 + m = 4.472135955

Solving
-6 + m = 4.472135955

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 = 4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + m = 4.472135955 + 6
m = 4.472135955 + 6

Combine like terms: 4.472135955 + 6 = 10.472135955
m = 10.472135955

Simplifying
m = 10.472135955


Subproblem 2
m + -6 = -4.472135955

Simplifying
m + -6 = -4.472135955

Reorder the terms:
-6 + m = -4.472135955

Solving
-6 + m = -4.472135955

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 = -4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + m = -4.472135955 + 6
m = -4.472135955 + 6

Combine like terms: -4.472135955 + 6 = 1.527864045
m = 1.527864045

Simplifying
m = 1.527864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {10.472135955, 1.527864045}
Solution
m = {10.472135955, 1.527864045}

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