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Simplifying 24r2 + 44r + -140 = 0 Reorder the terms: -140 + 44r + 24r2 = 0 Solving -140 + 44r + 24r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + 11r + 6r2) = 0 Factor a trinomial. 4((-7 + -2r)(5 + -3r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -2r)' equal to zero and attempt to solve: Simplifying -7 + -2r = 0 Solving -7 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2r = 0 + 7 -2r = 0 + 7 Combine like terms: 0 + 7 = 7 -2r = 7 Divide each side by '-2'. r = -3.5 Simplifying r = -3.5Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 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 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {-3.5, 1.666666667}
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