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Simplifying H(t) = 16t2 + 144t Multiply H * t tH = 16t2 + 144t Reorder the terms: tH = 144t + 16t2 Solving tH = 144t + 16t2 Solving for variable 't'. Reorder the terms: -144t + tH + -16t2 = 144t + 16t2 + -144t + -16t2 Reorder the terms: -144t + tH + -16t2 = 144t + -144t + 16t2 + -16t2 Combine like terms: 144t + -144t = 0 -144t + tH + -16t2 = 0 + 16t2 + -16t2 -144t + tH + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -144t + tH + -16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-144 + 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 '(-144 + H + -16t)' equal to zero and attempt to solve: Simplifying -144 + H + -16t = 0 Solving -144 + H + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '144' to each side of the equation. -144 + H + 144 + -16t = 0 + 144 Reorder the terms: -144 + 144 + H + -16t = 0 + 144 Combine like terms: -144 + 144 = 0 0 + H + -16t = 0 + 144 H + -16t = 0 + 144 Combine like terms: 0 + 144 = 144 H + -16t = 144 Add '-1H' to each side of the equation. H + -1H + -16t = 144 + -1H Combine like terms: H + -1H = 0 0 + -16t = 144 + -1H -16t = 144 + -1H Divide each side by '-16'. t = -9 + 0.0625H Simplifying t = -9 + 0.0625HSolution
t = {0, -9 + 0.0625H}
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