m^2+16m+21=0

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Solution for m^2+16m+21=0 equation: 


Simplifying
m2 + 16m + 21 = 0

Reorder the terms:
21 + 16m + m2 = 0

Solving
21 + 16m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 16m + -21 + m2 = 0 + -21

Reorder the terms:
21 + -21 + 16m + m2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 16m + m2 = 0 + -21
16m + m2 = 0 + -21

Combine like terms: 0 + -21 = -21
16m + m2 = -21

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 = -21 + 64

Reorder the terms:
64 + 16m + m2 = -21 + 64

Combine like terms: -21 + 64 = 43
64 + 16m + m2 = 43

Factor a perfect square on the left side:
(m + 8)(m + 8) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(m + 8) equal to 6.557438524 and -6.557438524.


Subproblem 1
m + 8 = 6.557438524

Simplifying
m + 8 = 6.557438524

Reorder the terms:
8 + m = 6.557438524

Solving
8 + m = 6.557438524

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 = 6.557438524 + -8

Combine like terms: 8 + -8 = 0
0 + m = 6.557438524 + -8
m = 6.557438524 + -8

Combine like terms: 6.557438524 + -8 = -1.442561476
m = -1.442561476

Simplifying
m = -1.442561476


Subproblem 2
m + 8 = -6.557438524

Simplifying
m + 8 = -6.557438524

Reorder the terms:
8 + m = -6.557438524

Solving
8 + m = -6.557438524

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 = -6.557438524 + -8

Combine like terms: 8 + -8 = 0
0 + m = -6.557438524 + -8
m = -6.557438524 + -8

Combine like terms: -6.557438524 + -8 = -14.557438524
m = -14.557438524

Simplifying
m = -14.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.442561476, -14.557438524}

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