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Simplifying -8r3 + 31r2 + -21r2 = 0 Reorder the terms: 31r2 + -21r2 + -8r3 = 0 Combine like terms: 31r2 + -21r2 = 10r2 10r2 + -8r3 = 0 Solving 10r2 + -8r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r2'. 2r2(5 + -4r) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve: Simplifying r2 = 0 Solving r2 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r2 = 0 Take the square root of each side: r = {0}Subproblem 2
Set the factor '(5 + -4r)' equal to zero and attempt to solve: Simplifying 5 + -4r = 0 Solving 5 + -4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4r = 0 + -5 -4r = 0 + -5 Combine like terms: 0 + -5 = -5 -4r = -5 Divide each side by '-4'. r = 1.25 Simplifying r = 1.25Solution
r = {0, 1.25}
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