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Simplifying 5r2 + -44r + 120 = 30 + 11r Reorder the terms: 120 + -44r + 5r2 = 30 + 11r Solving 120 + -44r + 5r2 = 30 + 11r Solving for variable 'r'. Reorder the terms: 120 + -30 + -44r + -11r + 5r2 = 30 + 11r + -30 + -11r Combine like terms: 120 + -30 = 90 90 + -44r + -11r + 5r2 = 30 + 11r + -30 + -11r Combine like terms: -44r + -11r = -55r 90 + -55r + 5r2 = 30 + 11r + -30 + -11r Reorder the terms: 90 + -55r + 5r2 = 30 + -30 + 11r + -11r Combine like terms: 30 + -30 = 0 90 + -55r + 5r2 = 0 + 11r + -11r 90 + -55r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 90 + -55r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(18 + -11r + r2) = 0 Factor a trinomial. 5((2 + -1r)(9 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {2, 9}
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