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Simplifying H(t) = -5t2 + 10t Multiply H * t tH = -5t2 + 10t Reorder the terms: tH = 10t + -5t2 Solving tH = 10t + -5t2 Solving for variable 't'. Reorder the terms: -10t + tH + 5t2 = 10t + -5t2 + -10t + 5t2 Reorder the terms: -10t + tH + 5t2 = 10t + -10t + -5t2 + 5t2 Combine like terms: 10t + -10t = 0 -10t + tH + 5t2 = 0 + -5t2 + 5t2 -10t + tH + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -10t + tH + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-10 + H + 5t) = 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 + 5t)' equal to zero and attempt to solve: Simplifying -10 + H + 5t = 0 Solving -10 + H + 5t = 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 + 5t = 0 + 10 Reorder the terms: -10 + 10 + H + 5t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + H + 5t = 0 + 10 H + 5t = 0 + 10 Combine like terms: 0 + 10 = 10 H + 5t = 10 Add '-1H' to each side of the equation. H + -1H + 5t = 10 + -1H Combine like terms: H + -1H = 0 0 + 5t = 10 + -1H 5t = 10 + -1H Divide each side by '5'. t = 2 + -0.2H Simplifying t = 2 + -0.2HSolution
t = {0, 2 + -0.2H}
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