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Simplifying 18r2 + 30r + 8 = 0 Reorder the terms: 8 + 30r + 18r2 = 0 Solving 8 + 30r + 18r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 15r + 9r2) = 0 Factor a trinomial. 2((4 + 3r)(1 + 3r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 3r)' equal to zero and attempt to solve: Simplifying 4 + 3r = 0 Solving 4 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3r = 0 + -4 3r = 0 + -4 Combine like terms: 0 + -4 = -4 3r = -4 Divide each side by '3'. r = -1.333333333 Simplifying r = -1.333333333Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve: Simplifying 1 + 3r = 0 Solving 1 + 3r = 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 + 3r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3r = 0 + -1 3r = 0 + -1 Combine like terms: 0 + -1 = -1 3r = -1 Divide each side by '3'. r = -0.3333333333 Simplifying r = -0.3333333333Solution
r = {-1.333333333, -0.3333333333}
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