15r^2-44r+120=-30+11r

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Solution for 15r^2-44r+120=-30+11r equation:


Simplifying
15r2 + -44r + 120 = -30 + 11r

Reorder the terms:
120 + -44r + 15r2 = -30 + 11r

Solving
120 + -44r + 15r2 = -30 + 11r

Solving for variable 'r'.

Reorder the terms:
120 + 30 + -44r + -11r + 15r2 = -30 + 11r + 30 + -11r

Combine like terms: 120 + 30 = 150
150 + -44r + -11r + 15r2 = -30 + 11r + 30 + -11r

Combine like terms: -44r + -11r = -55r
150 + -55r + 15r2 = -30 + 11r + 30 + -11r

Reorder the terms:
150 + -55r + 15r2 = -30 + 30 + 11r + -11r

Combine like terms: -30 + 30 = 0
150 + -55r + 15r2 = 0 + 11r + -11r
150 + -55r + 15r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
150 + -55r + 15r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + -11r + 3r2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(30 + -11r + 3r2)' equal to zero and attempt to solve: Simplifying 30 + -11r + 3r2 = 0 Solving 30 + -11r + 3r2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -3.666666667r + r2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -3.666666667r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + -3.666666667r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3.666666667r + r2 = 0 + -10 -3.666666667r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 -3.666666667r + r2 = -10 The r term is -3.666666667r. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667r + 3.361111114 + r2 = -10 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667r + r2 = -10 + 3.361111114 Combine like terms: -10 + 3.361111114 = -6.638888886 3.361111114 + -3.666666667r + r2 = -6.638888886 Factor a perfect square on the left side: (r + -1.833333334)(r + -1.833333334) = -6.638888886 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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