9r^2-18r-48=-9

Solution for 9r^2-18r-48=-9 equation:

Simplifying
9r2 + -18r + -48 = -9

Reorder the terms:
-48 + -18r + 9r2 = -9

Solving
-48 + -18r + 9r2 = -9

Solving for variable 'r'.

Reorder the terms:
-48 + 9 + -18r + 9r2 = -9 + 9

Combine like terms: -48 + 9 = -39
-39 + -18r + 9r2 = -9 + 9

Combine like terms: -9 + 9 = 0
-39 + -18r + 9r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + -6r + 3r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-13 + -6r + 3r2)' equal to zero and attempt to solve:

Simplifying
-13 + -6r + 3r2 = 0

Solving
-13 + -6r + 3r2 = 0

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

Divide each side by '3'.
-4.333333333 + -2r + r2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + -2r + 4.333333333 + r2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + -2r + r2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + -2r + r2 = 0 + 4.333333333
-2r + r2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
-2r + r2 = 4.333333333

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 4.333333333 + 1

Reorder the terms:
1 + -2r + r2 = 4.333333333 + 1

Combine like terms: 4.333333333 + 1 = 5.333333333
1 + -2r + r2 = 5.333333333

Factor a perfect square on the left side:
(r + -1)(r + -1) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(r + -1) equal to 2.309401077 and -2.309401077.

Subproblem 1
r + -1 = 2.309401077

Simplifying
r + -1 = 2.309401077

Reorder the terms:
-1 + r = 2.309401077

Solving
-1 + r = 2.309401077

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 2.309401077 + 1

Combine like terms: -1 + 1 = 0
0 + r = 2.309401077 + 1
r = 2.309401077 + 1

Combine like terms: 2.309401077 + 1 = 3.309401077
r = 3.309401077

Simplifying
r = 3.309401077

Subproblem 2
r + -1 = -2.309401077

Simplifying
r + -1 = -2.309401077

Reorder the terms:
-1 + r = -2.309401077

Solving
-1 + r = -2.309401077

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -2.309401077 + 1

Combine like terms: -1 + 1 = 0
0 + r = -2.309401077 + 1
r = -2.309401077 + 1

Combine like terms: -2.309401077 + 1 = -1.309401077
r = -1.309401077

Simplifying
r = -1.309401077

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.309401077, -1.309401077}
Solution
r = {3.309401077, -1.309401077}