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Simplifying H(t) = 56t + -16t2 + -16t2 + 56t Multiply H * t tH = 56t + -16t2 + -16t2 + 56t Reorder the terms: tH = 56t + 56t + -16t2 + -16t2 Combine like terms: 56t + 56t = 112t tH = 112t + -16t2 + -16t2 Combine like terms: -16t2 + -16t2 = -32t2 tH = 112t + -32t2 Solving tH = 112t + -32t2 Solving for variable 't'. Reorder the terms: -112t + tH + 32t2 = 112t + -32t2 + -112t + 32t2 Reorder the terms: -112t + tH + 32t2 = 112t + -112t + -32t2 + 32t2 Combine like terms: 112t + -112t = 0 -112t + tH + 32t2 = 0 + -32t2 + 32t2 -112t + tH + 32t2 = -32t2 + 32t2 Combine like terms: -32t2 + 32t2 = 0 -112t + tH + 32t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-112 + H + 32t) = 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 '(-112 + H + 32t)' equal to zero and attempt to solve: Simplifying -112 + H + 32t = 0 Solving -112 + H + 32t = 0 Move all terms containing t to the left, all other terms to the right. Add '112' to each side of the equation. -112 + H + 112 + 32t = 0 + 112 Reorder the terms: -112 + 112 + H + 32t = 0 + 112 Combine like terms: -112 + 112 = 0 0 + H + 32t = 0 + 112 H + 32t = 0 + 112 Combine like terms: 0 + 112 = 112 H + 32t = 112 Add '-1H' to each side of the equation. H + -1H + 32t = 112 + -1H Combine like terms: H + -1H = 0 0 + 32t = 112 + -1H 32t = 112 + -1H Divide each side by '32'. t = 3.5 + -0.03125H Simplifying t = 3.5 + -0.03125HSolution
t = {0, 3.5 + -0.03125H}
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