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Simplifying I(t) = -0.1t2 + 1.5t Multiply I * t tI = -0.1t2 + 1.5t Reorder the terms: tI = 1.5t + -0.1t2 Solving tI = 1.5t + -0.1t2 Solving for variable 't'. Reorder the terms: -1.5t + tI + 0.1t2 = 1.5t + -0.1t2 + -1.5t + 0.1t2 Reorder the terms: -1.5t + tI + 0.1t2 = 1.5t + -1.5t + -0.1t2 + 0.1t2 Combine like terms: 1.5t + -1.5t = 0.0 -1.5t + tI + 0.1t2 = 0.0 + -0.1t2 + 0.1t2 -1.5t + tI + 0.1t2 = -0.1t2 + 0.1t2 Combine like terms: -0.1t2 + 0.1t2 = 0.0 -1.5t + tI + 0.1t2 = 0.0 Factor out the Greatest Common Factor (GCF), 't'. t(-1.5 + I + 0.1t) = 0.0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-1.5 + I + 0.1t)' equal to zero and attempt to solve: Simplifying -1.5 + I + 0.1t = 0 Solving -1.5 + I + 0.1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + I + 1.5 + 0.1t = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + I + 0.1t = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + I + 0.1t = 0 + 1.5 I + 0.1t = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 I + 0.1t = 1.5 Add '-1I' to each side of the equation. I + -1I + 0.1t = 1.5 + -1I Combine like terms: I + -1I = 0 0 + 0.1t = 1.5 + -1I 0.1t = 1.5 + -1I Divide each side by '0.1'. t = 15 + -10I Simplifying t = 15 + -10ISolution
t = {0, 15 + -10I}
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