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Simplifying 6615 = 6000(1 + r)(1 + r) Multiply (1 + r) * (1 + r) 6615 = 6000(1(1 + r) + r(1 + r)) 6615 = 6000((1 * 1 + r * 1) + r(1 + r)) 6615 = 6000((1 + 1r) + r(1 + r)) 6615 = 6000(1 + 1r + (1 * r + r * r)) 6615 = 6000(1 + 1r + (1r + r2)) Combine like terms: 1r + 1r = 2r 6615 = 6000(1 + 2r + r2) 6615 = (1 * 6000 + 2r * 6000 + r2 * 6000) 6615 = (6000 + 12000r + 6000r2) Solving 6615 = 6000 + 12000r + 6000r2 Solving for variable 'r'. Combine like terms: 6615 + -6000 = 615 615 + -12000r + -6000r2 = 6000 + 12000r + 6000r2 + -6000 + -12000r + -6000r2 Reorder the terms: 615 + -12000r + -6000r2 = 6000 + -6000 + 12000r + -12000r + 6000r2 + -6000r2 Combine like terms: 6000 + -6000 = 0 615 + -12000r + -6000r2 = 0 + 12000r + -12000r + 6000r2 + -6000r2 615 + -12000r + -6000r2 = 12000r + -12000r + 6000r2 + -6000r2 Combine like terms: 12000r + -12000r = 0 615 + -12000r + -6000r2 = 0 + 6000r2 + -6000r2 615 + -12000r + -6000r2 = 6000r2 + -6000r2 Combine like terms: 6000r2 + -6000r2 = 0 615 + -12000r + -6000r2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(41 + -800r + -400r2) = 0 Factor a trinomial. 15((1 + -20r)(41 + 20r)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(1 + -20r)' equal to zero and attempt to solve: Simplifying 1 + -20r = 0 Solving 1 + -20r = 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 + -20r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -20r = 0 + -1 -20r = 0 + -1 Combine like terms: 0 + -1 = -1 -20r = -1 Divide each side by '-20'. r = 0.05 Simplifying r = 0.05Subproblem 2
Set the factor '(41 + 20r)' equal to zero and attempt to solve: Simplifying 41 + 20r = 0 Solving 41 + 20r = 0 Move all terms containing r to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + 20r = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 20r = 0 + -41 20r = 0 + -41 Combine like terms: 0 + -41 = -41 20r = -41 Divide each side by '20'. r = -2.05 Simplifying r = -2.05Solution
r = {0.05, -2.05}
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