H(t)=55t-16t^2

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Solution for H(t)=55t-16t^2 equation:


Simplifying
H(t) = 55t + -16t2

Multiply H * t
tH = 55t + -16t2

Solving
tH = 55t + -16t2

Solving for variable 't'.

Reorder the terms:
-55t + tH + 16t2 = 55t + -16t2 + -55t + 16t2

Reorder the terms:
-55t + tH + 16t2 = 55t + -55t + -16t2 + 16t2

Combine like terms: 55t + -55t = 0
-55t + tH + 16t2 = 0 + -16t2 + 16t2
-55t + tH + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-55t + tH + 16t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-55 + H + 16t) = 0

Subproblem 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 = 0

Subproblem 2

Set the factor '(-55 + H + 16t)' equal to zero and attempt to solve: Simplifying -55 + H + 16t = 0 Solving -55 + H + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '55' to each side of the equation. -55 + H + 55 + 16t = 0 + 55 Reorder the terms: -55 + 55 + H + 16t = 0 + 55 Combine like terms: -55 + 55 = 0 0 + H + 16t = 0 + 55 H + 16t = 0 + 55 Combine like terms: 0 + 55 = 55 H + 16t = 55 Add '-1H' to each side of the equation. H + -1H + 16t = 55 + -1H Combine like terms: H + -1H = 0 0 + 16t = 55 + -1H 16t = 55 + -1H Divide each side by '16'. t = 3.4375 + -0.0625H Simplifying t = 3.4375 + -0.0625H

Solution

t = {0, 3.4375 + -0.0625H}

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