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Simplifying H(t) = 68t + -8t2 Multiply H * t tH = 68t + -8t2 Solving tH = 68t + -8t2 Solving for variable 't'. Reorder the terms: -68t + tH + 8t2 = 68t + -8t2 + -68t + 8t2 Reorder the terms: -68t + tH + 8t2 = 68t + -68t + -8t2 + 8t2 Combine like terms: 68t + -68t = 0 -68t + tH + 8t2 = 0 + -8t2 + 8t2 -68t + tH + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -68t + tH + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-68 + 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 '(-68 + H + 8t)' equal to zero and attempt to solve: Simplifying -68 + H + 8t = 0 Solving -68 + H + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '68' to each side of the equation. -68 + H + 68 + 8t = 0 + 68 Reorder the terms: -68 + 68 + H + 8t = 0 + 68 Combine like terms: -68 + 68 = 0 0 + H + 8t = 0 + 68 H + 8t = 0 + 68 Combine like terms: 0 + 68 = 68 H + 8t = 68 Add '-1H' to each side of the equation. H + -1H + 8t = 68 + -1H Combine like terms: H + -1H = 0 0 + 8t = 68 + -1H 8t = 68 + -1H Divide each side by '8'. t = 8.5 + -0.125H Simplifying t = 8.5 + -0.125HSolution
t = {0, 8.5 + -0.125H}
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