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Simplifying H(t) = -10t2 + 260t Multiply H * t tH = -10t2 + 260t Reorder the terms: tH = 260t + -10t2 Solving tH = 260t + -10t2 Solving for variable 't'. Reorder the terms: -260t + tH + 10t2 = 260t + -10t2 + -260t + 10t2 Reorder the terms: -260t + tH + 10t2 = 260t + -260t + -10t2 + 10t2 Combine like terms: 260t + -260t = 0 -260t + tH + 10t2 = 0 + -10t2 + 10t2 -260t + tH + 10t2 = -10t2 + 10t2 Combine like terms: -10t2 + 10t2 = 0 -260t + tH + 10t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-260 + H + 10t) = 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 '(-260 + H + 10t)' equal to zero and attempt to solve: Simplifying -260 + H + 10t = 0 Solving -260 + H + 10t = 0 Move all terms containing t to the left, all other terms to the right. Add '260' to each side of the equation. -260 + H + 260 + 10t = 0 + 260 Reorder the terms: -260 + 260 + H + 10t = 0 + 260 Combine like terms: -260 + 260 = 0 0 + H + 10t = 0 + 260 H + 10t = 0 + 260 Combine like terms: 0 + 260 = 260 H + 10t = 260 Add '-1H' to each side of the equation. H + -1H + 10t = 260 + -1H Combine like terms: H + -1H = 0 0 + 10t = 260 + -1H 10t = 260 + -1H Divide each side by '10'. t = 26 + -0.1H Simplifying t = 26 + -0.1HSolution
t = {0, 26 + -0.1H}
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