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Simplifying 20 = 9r2 + -24r Reorder the terms: 20 = -24r + 9r2 Solving 20 = -24r + 9r2 Solving for variable 'r'. Reorder the terms: 20 + 24r + -9r2 = -24r + 24r + 9r2 + -9r2 Combine like terms: -24r + 24r = 0 20 + 24r + -9r2 = 0 + 9r2 + -9r2 20 + 24r + -9r2 = 9r2 + -9r2 Combine like terms: 9r2 + -9r2 = 0 20 + 24r + -9r2 = 0 Factor a trinomial. (10 + -3r)(2 + 3r) = 0Subproblem 1
Set the factor '(10 + -3r)' equal to zero and attempt to solve: Simplifying 10 + -3r = 0 Solving 10 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3r = 0 + -10 -3r = 0 + -10 Combine like terms: 0 + -10 = -10 -3r = -10 Divide each side by '-3'. r = 3.333333333 Simplifying r = 3.333333333Subproblem 2
Set the factor '(2 + 3r)' equal to zero and attempt to solve: Simplifying 2 + 3r = 0 Solving 2 + 3r = 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 + 3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3r = 0 + -2 3r = 0 + -2 Combine like terms: 0 + -2 = -2 3r = -2 Divide each side by '3'. r = -0.6666666667 Simplifying r = -0.6666666667Solution
r = {3.333333333, -0.6666666667}
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