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Simplifying 384 = -16t2 + 160t Reorder the terms: 384 = 160t + -16t2 Solving 384 = 160t + -16t2 Solving for variable 't'. Reorder the terms: 384 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 384 + -160t + 16t2 = 0 + -16t2 + 16t2 384 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 384 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(24 + -10t + t2) = 0 Factor a trinomial. 16((4 + -1t)(6 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {4, 6}
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