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Simplifying H(t) = -2t2 + 24t Multiply H * t tH = -2t2 + 24t Reorder the terms: tH = 24t + -2t2 Solving tH = 24t + -2t2 Solving for variable 't'. Reorder the terms: -24t + tH + 2t2 = 24t + -2t2 + -24t + 2t2 Reorder the terms: -24t + tH + 2t2 = 24t + -24t + -2t2 + 2t2 Combine like terms: 24t + -24t = 0 -24t + tH + 2t2 = 0 + -2t2 + 2t2 -24t + tH + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -24t + tH + 2t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-24 + H + 2t) = 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 '(-24 + H + 2t)' equal to zero and attempt to solve: Simplifying -24 + H + 2t = 0 Solving -24 + H + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '24' to each side of the equation. -24 + H + 24 + 2t = 0 + 24 Reorder the terms: -24 + 24 + H + 2t = 0 + 24 Combine like terms: -24 + 24 = 0 0 + H + 2t = 0 + 24 H + 2t = 0 + 24 Combine like terms: 0 + 24 = 24 H + 2t = 24 Add '-1H' to each side of the equation. H + -1H + 2t = 24 + -1H Combine like terms: H + -1H = 0 0 + 2t = 24 + -1H 2t = 24 + -1H Divide each side by '2'. t = 12 + -0.5H Simplifying t = 12 + -0.5HSolution
t = {0, 12 + -0.5H}
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