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Simplifying 22r2 + -80r + 46 = r2 + 4 + -3r Reorder the terms: 46 + -80r + 22r2 = r2 + 4 + -3r Reorder the terms: 46 + -80r + 22r2 = 4 + -3r + r2 Solving 46 + -80r + 22r2 = 4 + -3r + r2 Solving for variable 'r'. Reorder the terms: 46 + -4 + -80r + 3r + 22r2 + -1r2 = 4 + -3r + r2 + -4 + 3r + -1r2 Combine like terms: 46 + -4 = 42 42 + -80r + 3r + 22r2 + -1r2 = 4 + -3r + r2 + -4 + 3r + -1r2 Combine like terms: -80r + 3r = -77r 42 + -77r + 22r2 + -1r2 = 4 + -3r + r2 + -4 + 3r + -1r2 Combine like terms: 22r2 + -1r2 = 21r2 42 + -77r + 21r2 = 4 + -3r + r2 + -4 + 3r + -1r2 Reorder the terms: 42 + -77r + 21r2 = 4 + -4 + -3r + 3r + r2 + -1r2 Combine like terms: 4 + -4 = 0 42 + -77r + 21r2 = 0 + -3r + 3r + r2 + -1r2 42 + -77r + 21r2 = -3r + 3r + r2 + -1r2 Combine like terms: -3r + 3r = 0 42 + -77r + 21r2 = 0 + r2 + -1r2 42 + -77r + 21r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 42 + -77r + 21r2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(6 + -11r + 3r2) = 0 Factor a trinomial. 7((2 + -3r)(3 + -1r)) = 0 Ignore the factor 7.Subproblem 1
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 = 0.6666666667Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {0.6666666667, 3}
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