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Simplifying 38r + -12r2 + -16 = 0 Reorder the terms: -16 + 38r + -12r2 = 0 Solving -16 + 38r + -12r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 19r + -6r2) = 0 Factor a trinomial. 2((-8 + 3r)(1 + -2r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 3r)' equal to zero and attempt to solve: Simplifying -8 + 3r = 0 Solving -8 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3r = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3r = 0 + 8 3r = 0 + 8 Combine like terms: 0 + 8 = 8 3r = 8 Divide each side by '3'. r = 2.666666667 Simplifying r = 2.666666667Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 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 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {2.666666667, 0.5}
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