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Simplifying 8x = (1 + -1k)(1 + -1k)(1 + -1k) Multiply (1 + -1k) * (1 + -1k) 8x = (1(1 + -1k) + -1k * (1 + -1k))(1 + -1k) 8x = ((1 * 1 + -1k * 1) + -1k * (1 + -1k))(1 + -1k) 8x = ((1 + -1k) + -1k * (1 + -1k))(1 + -1k) 8x = (1 + -1k + (1 * -1k + -1k * -1k))(1 + -1k) 8x = (1 + -1k + (-1k + 1k2))(1 + -1k) Combine like terms: -1k + -1k = -2k 8x = (1 + -2k + 1k2)(1 + -1k) Multiply (1 + -2k + 1k2) * (1 + -1k) 8x = (1(1 + -1k) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) 8x = ((1 * 1 + -1k * 1) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) 8x = ((1 + -1k) + -2k * (1 + -1k) + 1k2 * (1 + -1k)) 8x = (1 + -1k + (1 * -2k + -1k * -2k) + 1k2 * (1 + -1k)) 8x = (1 + -1k + (-2k + 2k2) + 1k2 * (1 + -1k)) 8x = (1 + -1k + -2k + 2k2 + (1 * 1k2 + -1k * 1k2)) 8x = (1 + -1k + -2k + 2k2 + (1k2 + -1k3)) Combine like terms: -1k + -2k = -3k 8x = (1 + -3k + 2k2 + 1k2 + -1k3) Combine like terms: 2k2 + 1k2 = 3k2 8x = (1 + -3k + 3k2 + -1k3) Solving 8x = 1 + -3k + 3k2 + -1k3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '8'. x = 0.125 + -0.375k + 0.375k2 + -0.125k3 Simplifying x = 0.125 + -0.375k + 0.375k2 + -0.125k3
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