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Simplifying -4r2 + -83r + 83 = -12r + -11r2 + 11 Reorder the terms: 83 + -83r + -4r2 = -12r + -11r2 + 11 Reorder the terms: 83 + -83r + -4r2 = 11 + -12r + -11r2 Solving 83 + -83r + -4r2 = 11 + -12r + -11r2 Solving for variable 'r'. Reorder the terms: 83 + -11 + -83r + 12r + -4r2 + 11r2 = 11 + -12r + -11r2 + -11 + 12r + 11r2 Combine like terms: 83 + -11 = 72 72 + -83r + 12r + -4r2 + 11r2 = 11 + -12r + -11r2 + -11 + 12r + 11r2 Combine like terms: -83r + 12r = -71r 72 + -71r + -4r2 + 11r2 = 11 + -12r + -11r2 + -11 + 12r + 11r2 Combine like terms: -4r2 + 11r2 = 7r2 72 + -71r + 7r2 = 11 + -12r + -11r2 + -11 + 12r + 11r2 Reorder the terms: 72 + -71r + 7r2 = 11 + -11 + -12r + 12r + -11r2 + 11r2 Combine like terms: 11 + -11 = 0 72 + -71r + 7r2 = 0 + -12r + 12r + -11r2 + 11r2 72 + -71r + 7r2 = -12r + 12r + -11r2 + 11r2 Combine like terms: -12r + 12r = 0 72 + -71r + 7r2 = 0 + -11r2 + 11r2 72 + -71r + 7r2 = -11r2 + 11r2 Combine like terms: -11r2 + 11r2 = 0 72 + -71r + 7r2 = 0 Factor a trinomial. (8 + -7r)(9 + -1r) = 0Subproblem 1
Set the factor '(8 + -7r)' equal to zero and attempt to solve: Simplifying 8 + -7r = 0 Solving 8 + -7r = 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 + -7r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7r = 0 + -8 -7r = 0 + -8 Combine like terms: 0 + -8 = -8 -7r = -8 Divide each side by '-7'. r = 1.142857143 Simplifying r = 1.142857143Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {1.142857143, 9}
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