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Simplifying S(t) = -16t2 + 192t Multiply S * t tS = -16t2 + 192t Reorder the terms: tS = 192t + -16t2 Solving tS = 192t + -16t2 Solving for variable 't'. Reorder the terms: -192t + tS + 16t2 = 192t + -16t2 + -192t + 16t2 Reorder the terms: -192t + tS + 16t2 = 192t + -192t + -16t2 + 16t2 Combine like terms: 192t + -192t = 0 -192t + tS + 16t2 = 0 + -16t2 + 16t2 -192t + tS + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -192t + tS + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-192 + 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 '(-192 + S + 16t)' equal to zero and attempt to solve: Simplifying -192 + S + 16t = 0 Solving -192 + S + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '192' to each side of the equation. -192 + S + 192 + 16t = 0 + 192 Reorder the terms: -192 + 192 + S + 16t = 0 + 192 Combine like terms: -192 + 192 = 0 0 + S + 16t = 0 + 192 S + 16t = 0 + 192 Combine like terms: 0 + 192 = 192 S + 16t = 192 Add '-1S' to each side of the equation. S + -1S + 16t = 192 + -1S Combine like terms: S + -1S = 0 0 + 16t = 192 + -1S 16t = 192 + -1S Divide each side by '16'. t = 12 + -0.0625S Simplifying t = 12 + -0.0625SSolution
t = {0, 12 + -0.0625S}
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