r^2+8r-16=0

Solution for r^2+8r-16=0 equation:

Simplifying
r2 + 8r + -16 = 0

Reorder the terms:
-16 + 8r + r2 = 0

Solving
-16 + 8r + 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 + 8r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + 8r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 8r + r2 = 0 + 16
8r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
8r + r2 = 16

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 16 + 16

Reorder the terms:
16 + 8r + r2 = 16 + 16

Combine like terms: 16 + 16 = 32
16 + 8r + r2 = 32

Factor a perfect square on the left side:
(r + 4)(r + 4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(r + 4) equal to 5.656854249 and -5.656854249.

Subproblem 1
r + 4 = 5.656854249

Simplifying
r + 4 = 5.656854249

Reorder the terms:
4 + r = 5.656854249

Solving
4 + r = 5.656854249

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = 5.656854249 + -4

Combine like terms: 4 + -4 = 0
0 + r = 5.656854249 + -4
r = 5.656854249 + -4

Combine like terms: 5.656854249 + -4 = 1.656854249
r = 1.656854249

Simplifying
r = 1.656854249

Subproblem 2
r + 4 = -5.656854249

Simplifying
r + 4 = -5.656854249

Reorder the terms:
4 + r = -5.656854249

Solving
4 + r = -5.656854249

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = -5.656854249 + -4

Combine like terms: 4 + -4 = 0
0 + r = -5.656854249 + -4
r = -5.656854249 + -4

Combine like terms: -5.656854249 + -4 = -9.656854249
r = -9.656854249

Simplifying
r = -9.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.656854249, -9.656854249}