-72+11r+r^2=0

Solution for -72+11r+r^2=0 equation:

Simplifying
-72 + 11r + r2 = 0

Solving
-72 + 11r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + 11r + 72 + r2 = 0 + 72

Reorder the terms:
-72 + 72 + 11r + r2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + 11r + r2 = 0 + 72
11r + r2 = 0 + 72

Combine like terms: 0 + 72 = 72
11r + r2 = 72

The r term is 11r.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11r + 30.25 + r2 = 72 + 30.25

Reorder the terms:
30.25 + 11r + r2 = 72 + 30.25

Combine like terms: 72 + 30.25 = 102.25
30.25 + 11r + r2 = 102.25

Factor a perfect square on the left side:
(r + 5.5)(r + 5.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(r + 5.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
r + 5.5 = 10.111874208

Simplifying
r + 5.5 = 10.111874208

Reorder the terms:
5.5 + r = 10.111874208

Solving
5.5 + r = 10.111874208

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = 10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = 10.111874208 + -5.5
r = 10.111874208 + -5.5

Combine like terms: 10.111874208 + -5.5 = 4.611874208
r = 4.611874208

Simplifying
r = 4.611874208

Subproblem 2
r + 5.5 = -10.111874208

Simplifying
r + 5.5 = -10.111874208

Reorder the terms:
5.5 + r = -10.111874208

Solving
5.5 + r = -10.111874208

Solving for variable 'r'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + r = -10.111874208 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + r = -10.111874208 + -5.5
r = -10.111874208 + -5.5

Combine like terms: -10.111874208 + -5.5 = -15.611874208
r = -15.611874208

Simplifying
r = -15.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.611874208, -15.611874208}