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Simplifying 12r2 + -38r + 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((1 + -2r)(8 + -3r)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.5Subproblem 2
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 = 2.666666667Solution
r = {0.5, 2.666666667}
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