r^2+16r+16=0

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


Simplifying
r2 + 16r + 16 = 0

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

Solving
16 + 16r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -16 + 64

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

Combine like terms: -16 + 64 = 48
64 + 16r + r2 = 48

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

Calculate the square root of the right side: 6.92820323

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


Subproblem 1
r + 8 = 6.92820323

Simplifying
r + 8 = 6.92820323

Reorder the terms:
8 + r = 6.92820323

Solving
8 + r = 6.92820323

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 = 6.92820323 + -8

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

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

Simplifying
r = -1.07179677


Subproblem 2
r + 8 = -6.92820323

Simplifying
r + 8 = -6.92820323

Reorder the terms:
8 + r = -6.92820323

Solving
8 + r = -6.92820323

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 = -6.92820323 + -8

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

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

Simplifying
r = -14.92820323


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

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