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Simplifying 0 = 3r2 + 17r + 10 Reorder the terms: 0 = 10 + 17r + 3r2 Solving 0 = 10 + 17r + 3r2 Solving for variable 'r'. Combine like terms: 0 + -10 = -10 -10 + -17r + -3r2 = 10 + 17r + 3r2 + -10 + -17r + -3r2 Reorder the terms: -10 + -17r + -3r2 = 10 + -10 + 17r + -17r + 3r2 + -3r2 Combine like terms: 10 + -10 = 0 -10 + -17r + -3r2 = 0 + 17r + -17r + 3r2 + -3r2 -10 + -17r + -3r2 = 17r + -17r + 3r2 + -3r2 Combine like terms: 17r + -17r = 0 -10 + -17r + -3r2 = 0 + 3r2 + -3r2 -10 + -17r + -3r2 = 3r2 + -3r2 Combine like terms: 3r2 + -3r2 = 0 -10 + -17r + -3r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 17r + 3r2) = 0 Factor a trinomial. -1((5 + r)(2 + 3r)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Subproblem 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 = {-5, -0.6666666667}
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