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Simplifying 80 = 24t + -1t2 Solving 80 = 24t + -1t2 Solving for variable 't'. Reorder the terms: 80 + -24t + t2 = 24t + -24t + -1t2 + t2 Combine like terms: 24t + -24t = 0 80 + -24t + t2 = 0 + -1t2 + t2 80 + -24t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 80 + -24t + t2 = 0 Factor a trinomial. (4 + -1t)(20 + -1t) = 0Subproblem 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 '(20 + -1t)' equal to zero and attempt to solve: Simplifying 20 + -1t = 0 Solving 20 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1t = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1t = 0 + -20 -1t = 0 + -20 Combine like terms: 0 + -20 = -20 -1t = -20 Divide each side by '-1'. t = 20 Simplifying t = 20Solution
t = {4, 20}
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