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Simplifying H(t) = 60t + -1t2 Multiply H * t tH = 60t + -1t2 Solving tH = 60t + -1t2 Solving for variable 't'. Reorder the terms: -60t + tH + t2 = 60t + -1t2 + -60t + t2 Reorder the terms: -60t + tH + t2 = 60t + -60t + -1t2 + t2 Combine like terms: 60t + -60t = 0 -60t + tH + t2 = 0 + -1t2 + t2 -60t + tH + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -60t + tH + t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-60 + H + t) = 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 '(-60 + H + t)' equal to zero and attempt to solve: Simplifying -60 + H + t = 0 Solving -60 + H + t = 0 Move all terms containing t to the left, all other terms to the right. Add '60' to each side of the equation. -60 + H + 60 + t = 0 + 60 Reorder the terms: -60 + 60 + H + t = 0 + 60 Combine like terms: -60 + 60 = 0 0 + H + t = 0 + 60 H + t = 0 + 60 Combine like terms: 0 + 60 = 60 H + t = 60 Add '-1H' to each side of the equation. H + -1H + t = 60 + -1H Combine like terms: H + -1H = 0 0 + t = 60 + -1H t = 60 + -1H Simplifying t = 60 + -1HSolution
t = {0, 60 + -1H}
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