2m^2+32m+64=0

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Solution for 2m^2+32m+64=0 equation: 


Simplifying
2m2 + 32m + 64 = 0

Reorder the terms:
64 + 32m + 2m2 = 0

Solving
64 + 32m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + 16m + m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(32 + 16m + m2)' equal to zero and attempt to solve:

Simplifying
32 + 16m + m2 = 0

Solving
32 + 16m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 16m + -32 + m2 = 0 + -32

Reorder the terms:
32 + -32 + 16m + m2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 16m + m2 = 0 + -32
16m + m2 = 0 + -32

Combine like terms: 0 + -32 = -32
16m + m2 = -32

The m term is 16m.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16m + 64 + m2 = -32 + 64

Reorder the terms:
64 + 16m + m2 = -32 + 64

Combine like terms: -32 + 64 = 32
64 + 16m + m2 = 32

Factor a perfect square on the left side:
(m + 8)(m + 8) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(m + 8) equal to 5.656854249 and -5.656854249.


Subproblem 1
m + 8 = 5.656854249

Simplifying
m + 8 = 5.656854249

Reorder the terms:
8 + m = 5.656854249

Solving
8 + m = 5.656854249

Solving for variable 'm'.

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

Add '-8' to each side of the equation.
8 + -8 + m = 5.656854249 + -8

Combine like terms: 8 + -8 = 0
0 + m = 5.656854249 + -8
m = 5.656854249 + -8

Combine like terms: 5.656854249 + -8 = -2.343145751
m = -2.343145751

Simplifying
m = -2.343145751


Subproblem 2
m + 8 = -5.656854249

Simplifying
m + 8 = -5.656854249

Reorder the terms:
8 + m = -5.656854249

Solving
8 + m = -5.656854249

Solving for variable 'm'.

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

Add '-8' to each side of the equation.
8 + -8 + m = -5.656854249 + -8

Combine like terms: 8 + -8 = 0
0 + m = -5.656854249 + -8
m = -5.656854249 + -8

Combine like terms: -5.656854249 + -8 = -13.656854249
m = -13.656854249

Simplifying
m = -13.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-2.343145751, -13.656854249}
Solution
m = {-2.343145751, -13.656854249}

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