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Simplifying H(t) = -8t2 + -3t Multiply H * t tH = -8t2 + -3t Reorder the terms: tH = -3t + -8t2 Solving tH = -3t + -8t2 Solving for variable 't'. Reorder the terms: 3t + tH + 8t2 = -3t + -8t2 + 3t + 8t2 Reorder the terms: 3t + tH + 8t2 = -3t + 3t + -8t2 + 8t2 Combine like terms: -3t + 3t = 0 3t + tH + 8t2 = 0 + -8t2 + 8t2 3t + tH + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 3t + tH + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(3 + H + 8t) = 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 '(3 + H + 8t)' equal to zero and attempt to solve: Simplifying 3 + H + 8t = 0 Solving 3 + H + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + H + -3 + 8t = 0 + -3 Reorder the terms: 3 + -3 + H + 8t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + H + 8t = 0 + -3 H + 8t = 0 + -3 Combine like terms: 0 + -3 = -3 H + 8t = -3 Add '-1H' to each side of the equation. H + -1H + 8t = -3 + -1H Combine like terms: H + -1H = 0 0 + 8t = -3 + -1H 8t = -3 + -1H Divide each side by '8'. t = -0.375 + -0.125H Simplifying t = -0.375 + -0.125HSolution
t = {0, -0.375 + -0.125H}
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