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Simplifying S(t) = -16t2 + 144t Multiply S * t tS = -16t2 + 144t Reorder the terms: tS = 144t + -16t2 Solving tS = 144t + -16t2 Solving for variable 't'. Reorder the terms: -144t + tS + 16t2 = 144t + -16t2 + -144t + 16t2 Reorder the terms: -144t + tS + 16t2 = 144t + -144t + -16t2 + 16t2 Combine like terms: 144t + -144t = 0 -144t + tS + 16t2 = 0 + -16t2 + 16t2 -144t + tS + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144t + tS + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-144 + S + 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 '(-144 + S + 16t)' equal to zero and attempt to solve: Simplifying -144 + S + 16t = 0 Solving -144 + S + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '144' to each side of the equation. -144 + S + 144 + 16t = 0 + 144 Reorder the terms: -144 + 144 + S + 16t = 0 + 144 Combine like terms: -144 + 144 = 0 0 + S + 16t = 0 + 144 S + 16t = 0 + 144 Combine like terms: 0 + 144 = 144 S + 16t = 144 Add '-1S' to each side of the equation. S + -1S + 16t = 144 + -1S Combine like terms: S + -1S = 0 0 + 16t = 144 + -1S 16t = 144 + -1S Divide each side by '16'. t = 9 + -0.0625S Simplifying t = 9 + -0.0625SSolution
t = {0, 9 + -0.0625S}
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