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Simplifying 6 + -11r = 8r2 + 19r + 13 Reorder the terms: 6 + -11r = 13 + 19r + 8r2 Solving 6 + -11r = 13 + 19r + 8r2 Solving for variable 'r'. Reorder the terms: 6 + -13 + -11r + -19r + -8r2 = 13 + 19r + 8r2 + -13 + -19r + -8r2 Combine like terms: 6 + -13 = -7 -7 + -11r + -19r + -8r2 = 13 + 19r + 8r2 + -13 + -19r + -8r2 Combine like terms: -11r + -19r = -30r -7 + -30r + -8r2 = 13 + 19r + 8r2 + -13 + -19r + -8r2 Reorder the terms: -7 + -30r + -8r2 = 13 + -13 + 19r + -19r + 8r2 + -8r2 Combine like terms: 13 + -13 = 0 -7 + -30r + -8r2 = 0 + 19r + -19r + 8r2 + -8r2 -7 + -30r + -8r2 = 19r + -19r + 8r2 + -8r2 Combine like terms: 19r + -19r = 0 -7 + -30r + -8r2 = 0 + 8r2 + -8r2 -7 + -30r + -8r2 = 8r2 + -8r2 Combine like terms: 8r2 + -8r2 = 0 -7 + -30r + -8r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 30r + 8r2) = 0 Factor a trinomial. -1((7 + 2r)(1 + 4r)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 2r)' equal to zero and attempt to solve: Simplifying 7 + 2r = 0 Solving 7 + 2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2r = 0 + -7 2r = 0 + -7 Combine like terms: 0 + -7 = -7 2r = -7 Divide each side by '2'. r = -3.5 Simplifying r = -3.5Subproblem 2
Set the factor '(1 + 4r)' equal to zero and attempt to solve: Simplifying 1 + 4r = 0 Solving 1 + 4r = 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 + 4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4r = 0 + -1 4r = 0 + -1 Combine like terms: 0 + -1 = -1 4r = -1 Divide each side by '4'. r = -0.25 Simplifying r = -0.25Solution
r = {-3.5, -0.25}
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