5r^2-44r=-30+11r

Solution for 5r^2-44r=-30+11r equation:

Simplifying
5r2 + -44r = -30 + 11r

Reorder the terms:
-44r + 5r2 = -30 + 11r

Solving
-44r + 5r2 = -30 + 11r

Solving for variable 'r'.

Reorder the terms:
30 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r

Combine like terms: -44r + -11r = -55r
30 + -55r + 5r2 = -30 + 11r + 30 + -11r

Reorder the terms:
30 + -55r + 5r2 = -30 + 30 + 11r + -11r

Combine like terms: -30 + 30 = 0
30 + -55r + 5r2 = 0 + 11r + -11r
30 + -55r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
30 + -55r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -11r + r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + -11r + r2)' equal to zero and attempt to solve:

Simplifying
6 + -11r + r2 = 0

Solving
6 + -11r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -11r + -6 + r2 = 0 + -6

Reorder the terms:
6 + -6 + -11r + r2 = 0 + -6

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

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

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 = -6 + 30.25

Reorder the terms:
30.25 + -11r + r2 = -6 + 30.25

Combine like terms: -6 + 30.25 = 24.25
30.25 + -11r + r2 = 24.25

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(r + -5.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
r + -5.5 = 4.924428901

Simplifying
r + -5.5 = 4.924428901

Reorder the terms:
-5.5 + r = 4.924428901

Solving
-5.5 + r = 4.924428901

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 = 4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = 4.924428901 + 5.5
r = 4.924428901 + 5.5

Combine like terms: 4.924428901 + 5.5 = 10.424428901
r = 10.424428901

Simplifying
r = 10.424428901

Subproblem 2
r + -5.5 = -4.924428901

Simplifying
r + -5.5 = -4.924428901

Reorder the terms:
-5.5 + r = -4.924428901

Solving
-5.5 + r = -4.924428901

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 = -4.924428901 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = -4.924428901 + 5.5
r = -4.924428901 + 5.5

Combine like terms: -4.924428901 + 5.5 = 0.575571099
r = 0.575571099

Simplifying
r = 0.575571099

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10.424428901, 0.575571099}
Solution
r = {10.424428901, 0.575571099}