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Simplifying (-1t2 + 100t + 200)(-0.0001t2 + 0.02t + 0.5) = 0 Reorder the terms: (200 + 100t + -1t2)(-0.0001t2 + 0.02t + 0.5) = 0 Reorder the terms: (200 + 100t + -1t2)(0.5 + 0.02t + -0.0001t2) = 0 Multiply (200 + 100t + -1t2) * (0.5 + 0.02t + -0.0001t2) (200(0.5 + 0.02t + -0.0001t2) + 100t * (0.5 + 0.02t + -0.0001t2) + -1t2 * (0.5 + 0.02t + -0.0001t2)) = 0 ((0.5 * 200 + 0.02t * 200 + -0.0001t2 * 200) + 100t * (0.5 + 0.02t + -0.0001t2) + -1t2 * (0.5 + 0.02t + -0.0001t2)) = 0 ((100 + 4t + -0.02t2) + 100t * (0.5 + 0.02t + -0.0001t2) + -1t2 * (0.5 + 0.02t + -0.0001t2)) = 0 (100 + 4t + -0.02t2 + (0.5 * 100t + 0.02t * 100t + -0.0001t2 * 100t) + -1t2 * (0.5 + 0.02t + -0.0001t2)) = 0 (100 + 4t + -0.02t2 + (50t + 2t2 + -0.01t3) + -1t2 * (0.5 + 0.02t + -0.0001t2)) = 0 (100 + 4t + -0.02t2 + 50t + 2t2 + -0.01t3 + (0.5 * -1t2 + 0.02t * -1t2 + -0.0001t2 * -1t2)) = 0 (100 + 4t + -0.02t2 + 50t + 2t2 + -0.01t3 + (-0.5t2 + -0.02t3 + 0.0001t4)) = 0 Reorder the terms: (100 + 4t + 50t + -0.02t2 + 2t2 + -0.5t2 + -0.01t3 + -0.02t3 + 0.0001t4) = 0 Combine like terms: 4t + 50t = 54t (100 + 54t + -0.02t2 + 2t2 + -0.5t2 + -0.01t3 + -0.02t3 + 0.0001t4) = 0 Combine like terms: -0.02t2 + 2t2 = 1.98t2 (100 + 54t + 1.98t2 + -0.5t2 + -0.01t3 + -0.02t3 + 0.0001t4) = 0 Combine like terms: 1.98t2 + -0.5t2 = 1.48t2 (100 + 54t + 1.48t2 + -0.01t3 + -0.02t3 + 0.0001t4) = 0 Combine like terms: -0.01t3 + -0.02t3 = -0.03t3 (100 + 54t + 1.48t2 + -0.03t3 + 0.0001t4) = 0 Solving 100 + 54t + 1.48t2 + -0.03t3 + 0.0001t4 = 0 Solving for variable 't'. The solution to this equation could not be determined.
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