5-r^2-8r-11=0

Solution for 5-r^2-8r-11=0 equation:

Simplifying
5 + -1r2 + -8r + -11 = 0

Reorder the terms:
5 + -11 + -8r + -1r2 = 0

Combine like terms: 5 + -11 = -6
-6 + -8r + -1r2 = 0

Solving
-6 + -8r + -1r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 8r + r2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 8r + r2)' equal to zero and attempt to solve:

Simplifying
6 + 8r + r2 = 0

Solving
6 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 8r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + 8r + r2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 8r + r2 = 0 + -6
8r + r2 = 0 + -6

Combine like terms: 0 + -6 = -6
8r + r2 = -6

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 = -6 + 16

Reorder the terms:
16 + 8r + r2 = -6 + 16

Combine like terms: -6 + 16 = 10
16 + 8r + r2 = 10

Factor a perfect square on the left side:
(r + 4)(r + 4) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(r + 4) equal to 3.16227766 and -3.16227766.

Subproblem 1
r + 4 = 3.16227766

Simplifying
r + 4 = 3.16227766

Reorder the terms:
4 + r = 3.16227766

Solving
4 + r = 3.16227766

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 = 3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + r = 3.16227766 + -4
r = 3.16227766 + -4

Combine like terms: 3.16227766 + -4 = -0.83772234
r = -0.83772234

Simplifying
r = -0.83772234

Subproblem 2
r + 4 = -3.16227766

Simplifying
r + 4 = -3.16227766

Reorder the terms:
4 + r = -3.16227766

Solving
4 + r = -3.16227766

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 = -3.16227766 + -4

Combine like terms: 4 + -4 = 0
0 + r = -3.16227766 + -4
r = -3.16227766 + -4

Combine like terms: -3.16227766 + -4 = -7.16227766
r = -7.16227766

Simplifying
r = -7.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.83772234, -7.16227766}
Solution
r = {-0.83772234, -7.16227766}