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Simplifying 560 = 192t + -16t2 Solving 560 = 192t + -16t2 Solving for variable 't'. Reorder the terms: 560 + -192t + 16t2 = 192t + -192t + -16t2 + 16t2 Combine like terms: 192t + -192t = 0 560 + -192t + 16t2 = 0 + -16t2 + 16t2 560 + -192t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 560 + -192t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(35 + -12t + t2) = 0 Factor a trinomial. 16((5 + -1t)(7 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {5, 7}
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