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Simplifying H(t) = -5t2 + 45t Multiply H * t tH = -5t2 + 45t Reorder the terms: tH = 45t + -5t2 Solving tH = 45t + -5t2 Solving for variable 't'. Reorder the terms: -45t + tH + 5t2 = 45t + -5t2 + -45t + 5t2 Reorder the terms: -45t + tH + 5t2 = 45t + -45t + -5t2 + 5t2 Combine like terms: 45t + -45t = 0 -45t + tH + 5t2 = 0 + -5t2 + 5t2 -45t + tH + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -45t + tH + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-45 + 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 '(-45 + H + 5t)' equal to zero and attempt to solve: Simplifying -45 + H + 5t = 0 Solving -45 + H + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '45' to each side of the equation. -45 + H + 45 + 5t = 0 + 45 Reorder the terms: -45 + 45 + H + 5t = 0 + 45 Combine like terms: -45 + 45 = 0 0 + H + 5t = 0 + 45 H + 5t = 0 + 45 Combine like terms: 0 + 45 = 45 H + 5t = 45 Add '-1H' to each side of the equation. H + -1H + 5t = 45 + -1H Combine like terms: H + -1H = 0 0 + 5t = 45 + -1H 5t = 45 + -1H Divide each side by '5'. t = 9 + -0.2H Simplifying t = 9 + -0.2HSolution
t = {0, 9 + -0.2H}
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