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Simplifying H(t) = -16t2 + 42t + 0 Multiply H * t tH = -16t2 + 42t + 0 Reorder the terms: tH = 0 + 42t + -16t2 Remove the zero: tH = 42t + -16t2 Solving tH = 42t + -16t2 Solving for variable 't'. Reorder the terms: -42t + tH + 16t2 = 42t + -16t2 + -42t + 16t2 Reorder the terms: -42t + tH + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 -42t + tH + 16t2 = 0 + -16t2 + 16t2 -42t + tH + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -42t + tH + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-42 + 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 '(-42 + H + 16t)' equal to zero and attempt to solve: Simplifying -42 + H + 16t = 0 Solving -42 + H + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '42' to each side of the equation. -42 + H + 42 + 16t = 0 + 42 Reorder the terms: -42 + 42 + H + 16t = 0 + 42 Combine like terms: -42 + 42 = 0 0 + H + 16t = 0 + 42 H + 16t = 0 + 42 Combine like terms: 0 + 42 = 42 H + 16t = 42 Add '-1H' to each side of the equation. H + -1H + 16t = 42 + -1H Combine like terms: H + -1H = 0 0 + 16t = 42 + -1H 16t = 42 + -1H Divide each side by '16'. t = 2.625 + -0.0625H Simplifying t = 2.625 + -0.0625HSolution
t = {0, 2.625 + -0.0625H}
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