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Simplifying 10000(1 + r)(1 + r)(1 + r)(1 + r)(1 + r) = 86000 Multiply (1 + r) * (1 + r) 10000(1(1 + r) + r(1 + r))(1 + r)(1 + r)(1 + r) = 86000 10000((1 * 1 + r * 1) + r(1 + r))(1 + r)(1 + r)(1 + r) = 86000 10000((1 + 1r) + r(1 + r))(1 + r)(1 + r)(1 + r) = 86000 10000(1 + 1r + (1 * r + r * r))(1 + r)(1 + r)(1 + r) = 86000 10000(1 + 1r + (1r + r2))(1 + r)(1 + r)(1 + r) = 86000 Combine like terms: 1r + 1r = 2r 10000(1 + 2r + r2)(1 + r)(1 + r)(1 + r) = 86000 Multiply (1 + 2r + r2) * (1 + r) 10000(1(1 + r) + 2r * (1 + r) + r2(1 + r))(1 + r)(1 + r) = 86000 10000((1 * 1 + r * 1) + 2r * (1 + r) + r2(1 + r))(1 + r)(1 + r) = 86000 10000((1 + 1r) + 2r * (1 + r) + r2(1 + r))(1 + r)(1 + r) = 86000 10000(1 + 1r + (1 * 2r + r * 2r) + r2(1 + r))(1 + r)(1 + r) = 86000 10000(1 + 1r + (2r + 2r2) + r2(1 + r))(1 + r)(1 + r) = 86000 10000(1 + 1r + 2r + 2r2 + (1 * r2 + r * r2))(1 + r)(1 + r) = 86000 10000(1 + 1r + 2r + 2r2 + (1r2 + r3))(1 + r)(1 + r) = 86000 Combine like terms: 1r + 2r = 3r 10000(1 + 3r + 2r2 + 1r2 + r3)(1 + r)(1 + r) = 86000 Combine like terms: 2r2 + 1r2 = 3r2 10000(1 + 3r + 3r2 + r3)(1 + r)(1 + r) = 86000 Multiply (1 + 3r + 3r2 + r3) * (1 + r) 10000(1(1 + r) + 3r * (1 + r) + 3r2 * (1 + r) + r3(1 + r))(1 + r) = 86000 10000((1 * 1 + r * 1) + 3r * (1 + r) + 3r2 * (1 + r) + r3(1 + r))(1 + r) = 86000 10000((1 + 1r) + 3r * (1 + r) + 3r2 * (1 + r) + r3(1 + r))(1 + r) = 86000 10000(1 + 1r + (1 * 3r + r * 3r) + 3r2 * (1 + r) + r3(1 + r))(1 + r) = 86000 10000(1 + 1r + (3r + 3r2) + 3r2 * (1 + r) + r3(1 + r))(1 + r) = 86000 10000(1 + 1r + 3r + 3r2 + (1 * 3r2 + r * 3r2) + r3(1 + r))(1 + r) = 86000 10000(1 + 1r + 3r + 3r2 + (3r2 + 3r3) + r3(1 + r))(1 + r) = 86000 10000(1 + 1r + 3r + 3r2 + 3r2 + 3r3 + (1 * r3 + r * r3))(1 + r) = 86000 10000(1 + 1r + 3r + 3r2 + 3r2 + 3r3 + (1r3 + r4))(1 + r) = 86000 Combine like terms: 1r + 3r = 4r 10000(1 + 4r + 3r2 + 3r2 + 3r3 + 1r3 + r4)(1 + r) = 86000 Combine like terms: 3r2 + 3r2 = 6r2 10000(1 + 4r + 6r2 + 3r3 + 1r3 + r4)(1 + r) = 86000 Combine like terms: 3r3 + 1r3 = 4r3 10000(1 + 4r + 6r2 + 4r3 + r4)(1 + r) = 86000 Multiply (1 + 4r + 6r2 + 4r3 + r4) * (1 + r) 10000(1(1 + r) + 4r * (1 + r) + 6r2 * (1 + r) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000((1 * 1 + r * 1) + 4r * (1 + r) + 6r2 * (1 + r) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000((1 + 1r) + 4r * (1 + r) + 6r2 * (1 + r) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000(1 + 1r + (1 * 4r + r * 4r) + 6r2 * (1 + r) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000(1 + 1r + (4r + 4r2) + 6r2 * (1 + r) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000(1 + 1r + 4r + 4r2 + (1 * 6r2 + r * 6r2) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000(1 + 1r + 4r + 4r2 + (6r2 + 6r3) + 4r3 * (1 + r) + r4(1 + r)) = 86000 10000(1 + 1r + 4r + 4r2 + 6r2 + 6r3 + (1 * 4r3 + r * 4r3) + r4(1 + r)) = 86000 10000(1 + 1r + 4r + 4r2 + 6r2 + 6r3 + (4r3 + 4r4) + r4(1 + r)) = 86000 10000(1 + 1r + 4r + 4r2 + 6r2 + 6r3 + 4r3 + 4r4 + (1 * r4 + r * r4)) = 86000 10000(1 + 1r + 4r + 4r2 + 6r2 + 6r3 + 4r3 + 4r4 + (1r4 + r5)) = 86000 Combine like terms: 1r + 4r = 5r 10000(1 + 5r + 4r2 + 6r2 + 6r3 + 4r3 + 4r4 + 1r4 + r5) = 86000 Combine like terms: 4r2 + 6r2 = 10r2 10000(1 + 5r + 10r2 + 6r3 + 4r3 + 4r4 + 1r4 + r5) = 86000 Combine like terms: 6r3 + 4r3 = 10r3 10000(1 + 5r + 10r2 + 10r3 + 4r4 + 1r4 + r5) = 86000 Combine like terms: 4r4 + 1r4 = 5r4 10000(1 + 5r + 10r2 + 10r3 + 5r4 + r5) = 86000 (1 * 10000 + 5r * 10000 + 10r2 * 10000 + 10r3 * 10000 + 5r4 * 10000 + r5 * 10000) = 86000 (10000 + 50000r + 100000r2 + 100000r3 + 50000r4 + 10000r5) = 86000 Solving 10000 + 50000r + 100000r2 + 100000r3 + 50000r4 + 10000r5 = 86000 Solving for variable 'r'. Reorder the terms: 10000 + -86000 + 50000r + 100000r2 + 100000r3 + 50000r4 + 10000r5 = 86000 + -86000 Combine like terms: 10000 + -86000 = -76000 -76000 + 50000r + 100000r2 + 100000r3 + 50000r4 + 10000r5 = 86000 + -86000 Combine like terms: 86000 + -86000 = 0 -76000 + 50000r + 100000r2 + 100000r3 + 50000r4 + 10000r5 = 0 Factor out the Greatest Common Factor (GCF), '2000'. 2000(-38 + 25r + 50r2 + 50r3 + 25r4 + 5r5) = 0 Ignore the factor 2000.Subproblem 1
Set the factor '(-38 + 25r + 50r2 + 50r3 + 25r4 + 5r5)' equal to zero and attempt to solve: Simplifying -38 + 25r + 50r2 + 50r3 + 25r4 + 5r5 = 0 Solving -38 + 25r + 50r2 + 50r3 + 25r4 + 5r5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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