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Simplifying H(t) = -4t2 + 16t Multiply H * t tH = -4t2 + 16t Reorder the terms: tH = 16t + -4t2 Solving tH = 16t + -4t2 Solving for variable 't'. Reorder the terms: -16t + tH + 4t2 = 16t + -4t2 + -16t + 4t2 Reorder the terms: -16t + tH + 4t2 = 16t + -16t + -4t2 + 4t2 Combine like terms: 16t + -16t = 0 -16t + tH + 4t2 = 0 + -4t2 + 4t2 -16t + tH + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -16t + tH + 4t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-16 + H + 4t) = 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 '(-16 + H + 4t)' equal to zero and attempt to solve: Simplifying -16 + H + 4t = 0 Solving -16 + H + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '16' to each side of the equation. -16 + H + 16 + 4t = 0 + 16 Reorder the terms: -16 + 16 + H + 4t = 0 + 16 Combine like terms: -16 + 16 = 0 0 + H + 4t = 0 + 16 H + 4t = 0 + 16 Combine like terms: 0 + 16 = 16 H + 4t = 16 Add '-1H' to each side of the equation. H + -1H + 4t = 16 + -1H Combine like terms: H + -1H = 0 0 + 4t = 16 + -1H 4t = 16 + -1H Divide each side by '4'. t = 4 + -0.25H Simplifying t = 4 + -0.25HSolution
t = {0, 4 + -0.25H}
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