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Simplifying H(t) = -14t2 + 200t Multiply H * t tH = -14t2 + 200t Reorder the terms: tH = 200t + -14t2 Solving tH = 200t + -14t2 Solving for variable 't'. Reorder the terms: -200t + tH + 14t2 = 200t + -14t2 + -200t + 14t2 Reorder the terms: -200t + tH + 14t2 = 200t + -200t + -14t2 + 14t2 Combine like terms: 200t + -200t = 0 -200t + tH + 14t2 = 0 + -14t2 + 14t2 -200t + tH + 14t2 = -14t2 + 14t2 Combine like terms: -14t2 + 14t2 = 0 -200t + tH + 14t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-200 + H + 14t) = 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 '(-200 + H + 14t)' equal to zero and attempt to solve: Simplifying -200 + H + 14t = 0 Solving -200 + H + 14t = 0 Move all terms containing t to the left, all other terms to the right. Add '200' to each side of the equation. -200 + H + 200 + 14t = 0 + 200 Reorder the terms: -200 + 200 + H + 14t = 0 + 200 Combine like terms: -200 + 200 = 0 0 + H + 14t = 0 + 200 H + 14t = 0 + 200 Combine like terms: 0 + 200 = 200 H + 14t = 200 Add '-1H' to each side of the equation. H + -1H + 14t = 200 + -1H Combine like terms: H + -1H = 0 0 + 14t = 200 + -1H 14t = 200 + -1H Divide each side by '14'. t = 14.28571429 + -0.07142857143H Simplifying t = 14.28571429 + -0.07142857143HSolution
t = {0, 14.28571429 + -0.07142857143H}
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