r^2+16r+21=0

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


Simplifying
r2 + 16r + 21 = 0

Reorder the terms:
21 + 16r + r2 = 0

Solving
21 + 16r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 16r + -21 + r2 = 0 + -21

Reorder the terms:
21 + -21 + 16r + r2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 16r + r2 = 0 + -21
16r + r2 = 0 + -21

Combine like terms: 0 + -21 = -21
16r + r2 = -21

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

Add '64' to each side of the equation.
16r + 64 + r2 = -21 + 64

Reorder the terms:
64 + 16r + r2 = -21 + 64

Combine like terms: -21 + 64 = 43
64 + 16r + r2 = 43

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

Calculate the square root of the right side: 6.557438524

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


Subproblem 1
r + 8 = 6.557438524

Simplifying
r + 8 = 6.557438524

Reorder the terms:
8 + r = 6.557438524

Solving
8 + r = 6.557438524

Solving for variable 'r'.

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

Add '-8' to each side of the equation.
8 + -8 + r = 6.557438524 + -8

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

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

Simplifying
r = -1.442561476


Subproblem 2
r + 8 = -6.557438524

Simplifying
r + 8 = -6.557438524

Reorder the terms:
8 + r = -6.557438524

Solving
8 + r = -6.557438524

Solving for variable 'r'.

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

Add '-8' to each side of the equation.
8 + -8 + r = -6.557438524 + -8

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

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

Simplifying
r = -14.557438524


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

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