9r^2-20r-36=0

Solution for 9r^2-20r-36=0 equation:

Simplifying
9r2 + -20r + -36 = 0

Reorder the terms:
-36 + -20r + 9r2 = 0

Solving
-36 + -20r + 9r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-4 + -2.222222222r + r2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.222222222r + 4 + r2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.222222222r + r2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.222222222r + r2 = 0 + 4
-2.222222222r + r2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.222222222r + r2 = 4

The r term is -2.222222222r.  Take half its coefficient (-1.111111111).
Square it (1.234567901) and add it to both sides.

Add '1.234567901' to each side of the equation.
-2.222222222r + 1.234567901 + r2 = 4 + 1.234567901

Reorder the terms:
1.234567901 + -2.222222222r + r2 = 4 + 1.234567901

Combine like terms: 4 + 1.234567901 = 5.234567901
1.234567901 + -2.222222222r + r2 = 5.234567901

Factor a perfect square on the left side:
(r + -1.111111111)(r + -1.111111111) = 5.234567901

Calculate the square root of the right side: 2.287917809

Break this problem into two subproblems by setting 
(r + -1.111111111) equal to 2.287917809 and -2.287917809.

Subproblem 1
r + -1.111111111 = 2.287917809

Simplifying
r + -1.111111111 = 2.287917809

Reorder the terms:
-1.111111111 + r = 2.287917809

Solving
-1.111111111 + r = 2.287917809

Solving for variable 'r'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + r = 2.287917809 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + r = 2.287917809 + 1.111111111
r = 2.287917809 + 1.111111111

Combine like terms: 2.287917809 + 1.111111111 = 3.39902892
r = 3.39902892

Simplifying
r = 3.39902892

Subproblem 2
r + -1.111111111 = -2.287917809

Simplifying
r + -1.111111111 = -2.287917809

Reorder the terms:
-1.111111111 + r = -2.287917809

Solving
-1.111111111 + r = -2.287917809

Solving for variable 'r'.

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

Add '1.111111111' to each side of the equation.
-1.111111111 + 1.111111111 + r = -2.287917809 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + r = -2.287917809 + 1.111111111
r = -2.287917809 + 1.111111111

Combine like terms: -2.287917809 + 1.111111111 = -1.176806698
r = -1.176806698

Simplifying
r = -1.176806698

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.39902892, -1.176806698}