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Simplifying 140 = 140 + 38t + -16t2 Add '-140' to each side of the equation. 140 + -140 = 140 + 38t + -140 + -16t2 Combine like terms: 140 + -140 = 0 0 = 140 + 38t + -140 + -16t2 Reorder the terms: 0 = 140 + -140 + 38t + -16t2 Combine like terms: 140 + -140 = 0 0 = 0 + 38t + -16t2 0 = 38t + -16t2 Solving 0 = 38t + -16t2 Solving for variable 't'. Remove the zero: -38t + 16t2 = 38t + -16t2 + -38t + 16t2 Reorder the terms: -38t + 16t2 = 38t + -38t + -16t2 + 16t2 Combine like terms: 38t + -38t = 0 -38t + 16t2 = 0 + -16t2 + 16t2 -38t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -38t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-19 + 8t) = 0 Ignore the factor 2.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 = 0Subproblem 2
Set the factor '(-19 + 8t)' equal to zero and attempt to solve: Simplifying -19 + 8t = 0 Solving -19 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 8t = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 8t = 0 + 19 8t = 0 + 19 Combine like terms: 0 + 19 = 19 8t = 19 Divide each side by '8'. t = 2.375 Simplifying t = 2.375Solution
t = {0, 2.375}
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