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Simplifying H(t) = 16t(14 + -1t) Multiply H * t tH = 16t(14 + -1t) tH = (14 * 16t + -1t * 16t) tH = (224t + -16t2) Solving tH = 224t + -16t2 Solving for variable 't'. Reorder the terms: -224t + tH + 16t2 = 224t + -16t2 + -224t + 16t2 Reorder the terms: -224t + tH + 16t2 = 224t + -224t + -16t2 + 16t2 Combine like terms: 224t + -224t = 0 -224t + tH + 16t2 = 0 + -16t2 + 16t2 -224t + tH + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -224t + tH + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-224 + H + 16t) = 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 '(-224 + H + 16t)' equal to zero and attempt to solve: Simplifying -224 + H + 16t = 0 Solving -224 + H + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '224' to each side of the equation. -224 + H + 224 + 16t = 0 + 224 Reorder the terms: -224 + 224 + H + 16t = 0 + 224 Combine like terms: -224 + 224 = 0 0 + H + 16t = 0 + 224 H + 16t = 0 + 224 Combine like terms: 0 + 224 = 224 H + 16t = 224 Add '-1H' to each side of the equation. H + -1H + 16t = 224 + -1H Combine like terms: H + -1H = 0 0 + 16t = 224 + -1H 16t = 224 + -1H Divide each side by '16'. t = 14 + -0.0625H Simplifying t = 14 + -0.0625HSolution
t = {0, 14 + -0.0625H}
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