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Simplifying (1 + -1k)(1 + -1k)(1 + -1k) = 86 Multiply (1 + -1k) * (1 + -1k) (1(1 + -1k) + -1k * (1 + -1k))(1 + -1k) = 86 ((1 * 1 + -1k * 1) + -1k * (1 + -1k))(1 + -1k) = 86 ((1 + -1k) + -1k * (1 + -1k))(1 + -1k) = 86 (1 + -1k + (1 * -1k + -1k * -1k))(1 + -1k) = 86 (1 + -1k + (-1k + 1k2))(1 + -1k) = 86 Combine like terms: -1k + -1k = -2k (1 + -2k + 1k2)(1 + -1k) = 86 Multiply (1 + -2k + 1k2) * (1 + -1k) (1(1 + -1k) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) = 86 ((1 * 1 + -1k * 1) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) = 86 ((1 + -1k) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) = 86 (1 + -1k + (1 * -2k + -1k * -2k) + 1k2 * (1 + -1k)) = 86 (1 + -1k + (-2k + 2k2) + 1k2 * (1 + -1k)) = 86 (1 + -1k + -2k + 2k2 + (1 * 1k2 + -1k * 1k2)) = 86 (1 + -1k + -2k + 2k2 + (1k2 + -1k3)) = 86 Combine like terms: -1k + -2k = -3k (1 + -3k + 2k2 + 1k2 + -1k3) = 86 Combine like terms: 2k2 + 1k2 = 3k2 (1 + -3k + 3k2 + -1k3) = 86 Solving 1 + -3k + 3k2 + -1k3 = 86 Solving for variable 'k'. Reorder the terms: 1 + -86 + -3k + 3k2 + -1k3 = 86 + -86 Combine like terms: 1 + -86 = -85 -85 + -3k + 3k2 + -1k3 = 86 + -86 Combine like terms: 86 + -86 = 0 -85 + -3k + 3k2 + -1k3 = 0 The solution to this equation could not be determined.
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