m^2+16m+5=-11

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Solution for m^2+16m+5=-11 equation: 


Simplifying
m2 + 16m + 5 = -11

Reorder the terms:
5 + 16m + m2 = -11

Solving
5 + 16m + m2 = -11

Solving for variable 'm'.

Reorder the terms:
5 + 11 + 16m + m2 = -11 + 11

Combine like terms: 5 + 11 = 16
16 + 16m + m2 = -11 + 11

Combine like terms: -11 + 11 = 0
16 + 16m + m2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -16 + 64

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

Combine like terms: -16 + 64 = 48
64 + 16m + m2 = 48

Factor a perfect square on the left side:
(m + 8)(m + 8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(m + 8) equal to 6.92820323 and -6.92820323.


Subproblem 1
m + 8 = 6.92820323

Simplifying
m + 8 = 6.92820323

Reorder the terms:
8 + m = 6.92820323

Solving
8 + m = 6.92820323

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 = 6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + m = 6.92820323 + -8
m = 6.92820323 + -8

Combine like terms: 6.92820323 + -8 = -1.07179677
m = -1.07179677

Simplifying
m = -1.07179677


Subproblem 2
m + 8 = -6.92820323

Simplifying
m + 8 = -6.92820323

Reorder the terms:
8 + m = -6.92820323

Solving
8 + m = -6.92820323

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 = -6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + m = -6.92820323 + -8
m = -6.92820323 + -8

Combine like terms: -6.92820323 + -8 = -14.92820323
m = -14.92820323

Simplifying
m = -14.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.07179677, -14.92820323}

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