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Simplifying -2r2 + 11r + 24 = 11 Reorder the terms: 24 + 11r + -2r2 = 11 Solving 24 + 11r + -2r2 = 11 Solving for variable 'r'. Reorder the terms: 24 + -11 + 11r + -2r2 = 11 + -11 Combine like terms: 24 + -11 = 13 13 + 11r + -2r2 = 11 + -11 Combine like terms: 11 + -11 = 0 13 + 11r + -2r2 = 0 Factor a trinomial. (13 + -2r)(1 + r) = 0Subproblem 1
Set the factor '(13 + -2r)' equal to zero and attempt to solve: Simplifying 13 + -2r = 0 Solving 13 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2r = 0 + -13 -2r = 0 + -13 Combine like terms: 0 + -13 = -13 -2r = -13 Divide each side by '-2'. r = 6.5 Simplifying r = 6.5Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve: Simplifying 1 + r = 0 Solving 1 + r = 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 + r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r = 0 + -1 r = 0 + -1 Combine like terms: 0 + -1 = -1 r = -1 Simplifying r = -1Solution
r = {6.5, -1}
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