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Simplifying 576 = -16t2 + 96t + 432 Reorder the terms: 576 = 432 + 96t + -16t2 Solving 576 = 432 + 96t + -16t2 Solving for variable 't'. Combine like terms: 576 + -432 = 144 144 + -96t + 16t2 = 432 + 96t + -16t2 + -432 + -96t + 16t2 Reorder the terms: 144 + -96t + 16t2 = 432 + -432 + 96t + -96t + -16t2 + 16t2 Combine like terms: 432 + -432 = 0 144 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 144 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 144 + -96t + 16t2 = 0 + -16t2 + 16t2 144 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 144 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(9 + -6t + t2) = 0 Factor a trinomial. 16((3 + -1t)(3 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {3, 3}
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