5r^2-44r+120=-33+11r

Solution for 5r^2-44r+120=-33+11r equation:

Simplifying
5r2 + -44r + 120 = -33 + 11r

Reorder the terms:
120 + -44r + 5r2 = -33 + 11r

Solving
120 + -44r + 5r2 = -33 + 11r

Solving for variable 'r'.

Reorder the terms:
120 + 33 + -44r + -11r + 5r2 = -33 + 11r + 33 + -11r

Combine like terms: 120 + 33 = 153
153 + -44r + -11r + 5r2 = -33 + 11r + 33 + -11r

Combine like terms: -44r + -11r = -55r
153 + -55r + 5r2 = -33 + 11r + 33 + -11r

Reorder the terms:
153 + -55r + 5r2 = -33 + 33 + 11r + -11r

Combine like terms: -33 + 33 = 0
153 + -55r + 5r2 = 0 + 11r + -11r
153 + -55r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
153 + -55r + 5r2 = 0

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

Divide each side by '5'.
30.6 + -11r + r2 = 0

Move the constant term to the right:

Add '-30.6' to each side of the equation.
30.6 + -11r + -30.6 + r2 = 0 + -30.6

Reorder the terms:
30.6 + -30.6 + -11r + r2 = 0 + -30.6

Combine like terms: 30.6 + -30.6 = 0.0
0.0 + -11r + r2 = 0 + -30.6
-11r + r2 = 0 + -30.6

Combine like terms: 0 + -30.6 = -30.6
-11r + r2 = -30.6

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 = -30.6 + 30.25

Reorder the terms:
30.25 + -11r + r2 = -30.6 + 30.25

Combine like terms: -30.6 + 30.25 = -0.35
30.25 + -11r + r2 = -0.35

Factor a perfect square on the left side:
(r + -5.5)(r + -5.5) = -0.35

Can't calculate square root of the right side.

The solution to this equation could not be determined.