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Simplifying 5 = r(2r + 3) Reorder the terms: 5 = r(3 + 2r) 5 = (3 * r + 2r * r) 5 = (3r + 2r2) Solving 5 = 3r + 2r2 Solving for variable 'r'. Reorder the terms: 5 + -3r + -2r2 = 3r + -3r + 2r2 + -2r2 Combine like terms: 3r + -3r = 0 5 + -3r + -2r2 = 0 + 2r2 + -2r2 5 + -3r + -2r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 5 + -3r + -2r2 = 0 Factor a trinomial. (1 + -1r)(5 + 2r) = 0Subproblem 1
Set the factor '(1 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 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 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Subproblem 2
Set the factor '(5 + 2r)' equal to zero and attempt to solve: Simplifying 5 + 2r = 0 Solving 5 + 2r = 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 + 2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2r = 0 + -5 2r = 0 + -5 Combine like terms: 0 + -5 = -5 2r = -5 Divide each side by '2'. r = -2.5 Simplifying r = -2.5Solution
r = {1, -2.5}
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