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Simplifying 18r3 + -34r2 + 16r = 0 Reorder the terms: 16r + -34r2 + 18r3 = 0 Solving 16r + -34r2 + 18r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(8 + -17r + 9r2) = 0 Factor a trinomial. 2r((8 + -9r)(1 + -1r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(8 + -9r)' equal to zero and attempt to solve: Simplifying 8 + -9r = 0 Solving 8 + -9r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -9r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9r = 0 + -8 -9r = 0 + -8 Combine like terms: 0 + -8 = -8 -9r = -8 Divide each side by '-9'. r = 0.8888888889 Simplifying r = 0.8888888889Subproblem 3
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {0, 0.8888888889, 1}
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