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Simplifying H(t) = -8t2 + 32t Multiply H * t tH = -8t2 + 32t Reorder the terms: tH = 32t + -8t2 Solving tH = 32t + -8t2 Solving for variable 't'. Reorder the terms: -32t + tH + 8t2 = 32t + -8t2 + -32t + 8t2 Reorder the terms: -32t + tH + 8t2 = 32t + -32t + -8t2 + 8t2 Combine like terms: 32t + -32t = 0 -32t + tH + 8t2 = 0 + -8t2 + 8t2 -32t + tH + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -32t + tH + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-32 + 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 '(-32 + H + 8t)' equal to zero and attempt to solve: Simplifying -32 + H + 8t = 0 Solving -32 + H + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '32' to each side of the equation. -32 + H + 32 + 8t = 0 + 32 Reorder the terms: -32 + 32 + H + 8t = 0 + 32 Combine like terms: -32 + 32 = 0 0 + H + 8t = 0 + 32 H + 8t = 0 + 32 Combine like terms: 0 + 32 = 32 H + 8t = 32 Add '-1H' to each side of the equation. H + -1H + 8t = 32 + -1H Combine like terms: H + -1H = 0 0 + 8t = 32 + -1H 8t = 32 + -1H Divide each side by '8'. t = 4 + -0.125H Simplifying t = 4 + -0.125HSolution
t = {0, 4 + -0.125H}
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