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Simplifying H(t) = -5t2 + -30t Multiply H * t tH = -5t2 + -30t Reorder the terms: tH = -30t + -5t2 Solving tH = -30t + -5t2 Solving for variable 't'. Reorder the terms: 30t + tH + 5t2 = -30t + -5t2 + 30t + 5t2 Reorder the terms: 30t + tH + 5t2 = -30t + 30t + -5t2 + 5t2 Combine like terms: -30t + 30t = 0 30t + tH + 5t2 = 0 + -5t2 + 5t2 30t + tH + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 30t + tH + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(30 + 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 '(30 + H + 5t)' equal to zero and attempt to solve: Simplifying 30 + H + 5t = 0 Solving 30 + H + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + H + -30 + 5t = 0 + -30 Reorder the terms: 30 + -30 + H + 5t = 0 + -30 Combine like terms: 30 + -30 = 0 0 + H + 5t = 0 + -30 H + 5t = 0 + -30 Combine like terms: 0 + -30 = -30 H + 5t = -30 Add '-1H' to each side of the equation. H + -1H + 5t = -30 + -1H Combine like terms: H + -1H = 0 0 + 5t = -30 + -1H 5t = -30 + -1H Divide each side by '5'. t = -6 + -0.2H Simplifying t = -6 + -0.2HSolution
t = {0, -6 + -0.2H}
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