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Simplifying H(t) = 50t + -5t2 Multiply H * t tH = 50t + -5t2 Solving tH = 50t + -5t2 Solving for variable 't'. Reorder the terms: -50t + tH + 5t2 = 50t + -5t2 + -50t + 5t2 Reorder the terms: -50t + tH + 5t2 = 50t + -50t + -5t2 + 5t2 Combine like terms: 50t + -50t = 0 -50t + tH + 5t2 = 0 + -5t2 + 5t2 -50t + tH + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -50t + tH + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-50 + 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 '(-50 + H + 5t)' equal to zero and attempt to solve: Simplifying -50 + H + 5t = 0 Solving -50 + H + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + H + 50 + 5t = 0 + 50 Reorder the terms: -50 + 50 + H + 5t = 0 + 50 Combine like terms: -50 + 50 = 0 0 + H + 5t = 0 + 50 H + 5t = 0 + 50 Combine like terms: 0 + 50 = 50 H + 5t = 50 Add '-1H' to each side of the equation. H + -1H + 5t = 50 + -1H Combine like terms: H + -1H = 0 0 + 5t = 50 + -1H 5t = 50 + -1H Divide each side by '5'. t = 10 + -0.2H Simplifying t = 10 + -0.2HSolution
t = {0, 10 + -0.2H}
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