5r^2-44r+20=30+11r

Solution for 5r^2-44r+20=30+11r equation:

Simplifying
5r2 + -44r + 20 = 30 + 11r

Reorder the terms:
20 + -44r + 5r2 = 30 + 11r

Solving
20 + -44r + 5r2 = 30 + 11r

Solving for variable 'r'.

Reorder the terms:
20 + -30 + -44r + -11r + 5r2 = 30 + 11r + -30 + -11r

Combine like terms: 20 + -30 = -10
-10 + -44r + -11r + 5r2 = 30 + 11r + -30 + -11r

Combine like terms: -44r + -11r = -55r
-10 + -55r + 5r2 = 30 + 11r + -30 + -11r

Reorder the terms:
-10 + -55r + 5r2 = 30 + -30 + 11r + -11r

Combine like terms: 30 + -30 = 0
-10 + -55r + 5r2 = 0 + 11r + -11r
-10 + -55r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-10 + -55r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + -11r + r2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-2 + -11r + r2)' equal to zero and attempt to solve:

Simplifying
-2 + -11r + r2 = 0

Solving
-2 + -11r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -11r + 2 + r2 = 0 + 2

Reorder the terms:
-2 + 2 + -11r + r2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -11r + r2 = 0 + 2
-11r + r2 = 0 + 2

Combine like terms: 0 + 2 = 2
-11r + r2 = 2

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 = 2 + 30.25

Reorder the terms:
30.25 + -11r + r2 = 2 + 30.25

Combine like terms: 2 + 30.25 = 32.25
30.25 + -11r + r2 = 32.25

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(r + -5.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
r + -5.5 = 5.678908346

Simplifying
r + -5.5 = 5.678908346

Reorder the terms:
-5.5 + r = 5.678908346

Solving
-5.5 + r = 5.678908346

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 = 5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = 5.678908346 + 5.5
r = 5.678908346 + 5.5

Combine like terms: 5.678908346 + 5.5 = 11.178908346
r = 11.178908346

Simplifying
r = 11.178908346

Subproblem 2
r + -5.5 = -5.678908346

Simplifying
r + -5.5 = -5.678908346

Reorder the terms:
-5.5 + r = -5.678908346

Solving
-5.5 + r = -5.678908346

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 = -5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + r = -5.678908346 + 5.5
r = -5.678908346 + 5.5

Combine like terms: -5.678908346 + 5.5 = -0.178908346
r = -0.178908346

Simplifying
r = -0.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.178908346, -0.178908346}
Solution
r = {11.178908346, -0.178908346}