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Simplifying 81r3 + -1r = 0 Reorder the terms: -1r + 81r3 = 0 Solving -1r + 81r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-1 + 81r2) = 0 Factor a difference between two squares. r((1 + 9r)(-1 + 9r)) = 0Subproblem 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 '(1 + 9r)' equal to zero and attempt to solve: Simplifying 1 + 9r = 0 Solving 1 + 9r = 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 + 9r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9r = 0 + -1 9r = 0 + -1 Combine like terms: 0 + -1 = -1 9r = -1 Divide each side by '9'. r = -0.1111111111 Simplifying r = -0.1111111111Subproblem 3
Set the factor '(-1 + 9r)' equal to zero and attempt to solve: Simplifying -1 + 9r = 0 Solving -1 + 9r = 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 + 9r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9r = 0 + 1 9r = 0 + 1 Combine like terms: 0 + 1 = 1 9r = 1 Divide each side by '9'. r = 0.1111111111 Simplifying r = 0.1111111111Solution
r = {0, -0.1111111111, 0.1111111111}
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