m^2+16m+8=0

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Solution for m^2+16m+8=0 equation: 


Simplifying
m2 + 16m + 8 = 0

Reorder the terms:
8 + 16m + m2 = 0

Solving
8 + 16m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 16m + -8 + m2 = 0 + -8

Reorder the terms:
8 + -8 + 16m + m2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 16m + m2 = 0 + -8
16m + m2 = 0 + -8

Combine like terms: 0 + -8 = -8
16m + m2 = -8

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 = -8 + 64

Reorder the terms:
64 + 16m + m2 = -8 + 64

Combine like terms: -8 + 64 = 56
64 + 16m + m2 = 56

Factor a perfect square on the left side:
(m + 8)(m + 8) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(m + 8) equal to 7.483314774 and -7.483314774.


Subproblem 1
m + 8 = 7.483314774

Simplifying
m + 8 = 7.483314774

Reorder the terms:
8 + m = 7.483314774

Solving
8 + m = 7.483314774

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 = 7.483314774 + -8

Combine like terms: 8 + -8 = 0
0 + m = 7.483314774 + -8
m = 7.483314774 + -8

Combine like terms: 7.483314774 + -8 = -0.516685226
m = -0.516685226

Simplifying
m = -0.516685226


Subproblem 2
m + 8 = -7.483314774

Simplifying
m + 8 = -7.483314774

Reorder the terms:
8 + m = -7.483314774

Solving
8 + m = -7.483314774

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 = -7.483314774 + -8

Combine like terms: 8 + -8 = 0
0 + m = -7.483314774 + -8
m = -7.483314774 + -8

Combine like terms: -7.483314774 + -8 = -15.483314774
m = -15.483314774

Simplifying
m = -15.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.516685226, -15.483314774}

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