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Simplifying (1 + -1t)(1 + -1t)(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 Multiply (1 + -1t) * (1 + -1t) (1(1 + -1t) + -1t * (1 + -1t))(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 ((1 * 1 + -1t * 1) + -1t * (1 + -1t))(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 ((1 + -1t) + -1t * (1 + -1t))(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + -1t + (1 * -1t + -1t * -1t))(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + -1t + (-1t + 1t2))(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 Combine like terms: -1t + -1t = -2t (1 + -2t + 1t2)(1 + t) + 2 + -1[(1 + t)(1 + -1t)] = 0 Multiply (1 + -2t + 1t2) * (1 + t) (1(1 + t) + -2t * (1 + t) + 1t2 * (1 + t)) + 2 + -1[(1 + t)(1 + -1t)] = 0 ((1 * 1 + t * 1) + -2t * (1 + t) + 1t2 * (1 + t)) + 2 + -1[(1 + t)(1 + -1t)] = 0 ((1 + 1t) + -2t * (1 + t) + 1t2 * (1 + t)) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + 1t + (1 * -2t + t * -2t) + 1t2 * (1 + t)) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + 1t + (-2t + -2t2) + 1t2 * (1 + t)) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + 1t + -2t + -2t2 + (1 * 1t2 + t * 1t2)) + 2 + -1[(1 + t)(1 + -1t)] = 0 (1 + 1t + -2t + -2t2 + (1t2 + 1t3)) + 2 + -1[(1 + t)(1 + -1t)] = 0 Combine like terms: 1t + -2t = -1t (1 + -1t + -2t2 + 1t2 + 1t3) + 2 + -1[(1 + t)(1 + -1t)] = 0 Combine like terms: -2t2 + 1t2 = -1t2 (1 + -1t + -1t2 + 1t3) + 2 + -1[(1 + t)(1 + -1t)] = 0 Multiply (1 + t) * (1 + -1t) 1 + -1t + -1t2 + 1t3 + 2 + -1[(1(1 + -1t) + t(1 + -1t))] = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[((1 * 1 + -1t * 1) + t(1 + -1t))] = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[((1 + -1t) + t(1 + -1t))] = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[(1 + -1t + (1 * t + -1t * t))] = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[(1 + -1t + (1t + -1t2))] = 0 Combine like terms: -1t + 1t = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[(1 + 0 + -1t2)] = 0 1 + -1t + -1t2 + 1t3 + 2 + -1[(1 + -1t2)] = 0 1 + -1t + -1t2 + 1t3 + 2 + [1 * -1 + -1t2 * -1] = 0 1 + -1t + -1t2 + 1t3 + 2 + [-1 + 1t2] = 0 Reorder the terms: 1 + 2 + -1 + -1t + -1t2 + 1t2 + 1t3 = 0 Combine like terms: 1 + 2 = 3 3 + -1 + -1t + -1t2 + 1t2 + 1t3 = 0 Combine like terms: 3 + -1 = 2 2 + -1t + -1t2 + 1t2 + 1t3 = 0 Combine like terms: -1t2 + 1t2 = 0 2 + -1t + 0 + 1t3 = 0 2 + -1t + 1t3 = 0 Solving 2 + -1t + 1t3 = 0 Solving for variable 't'. The solution to this equation could not be determined.
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