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Simplifying H(t) = 10t + -2t2 Multiply H * t tH = 10t + -2t2 Solving tH = 10t + -2t2 Solving for variable 't'. Reorder the terms: -10t + tH + 2t2 = 10t + -2t2 + -10t + 2t2 Reorder the terms: -10t + tH + 2t2 = 10t + -10t + -2t2 + 2t2 Combine like terms: 10t + -10t = 0 -10t + tH + 2t2 = 0 + -2t2 + 2t2 -10t + tH + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -10t + tH + 2t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-10 + 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 '(-10 + H + 2t)' equal to zero and attempt to solve: Simplifying -10 + H + 2t = 0 Solving -10 + H + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + H + 10 + 2t = 0 + 10 Reorder the terms: -10 + 10 + H + 2t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + H + 2t = 0 + 10 H + 2t = 0 + 10 Combine like terms: 0 + 10 = 10 H + 2t = 10 Add '-1H' to each side of the equation. H + -1H + 2t = 10 + -1H Combine like terms: H + -1H = 0 0 + 2t = 10 + -1H 2t = 10 + -1H Divide each side by '2'. t = 5 + -0.5H Simplifying t = 5 + -0.5HSolution
t = {0, 5 + -0.5H}
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