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Simplifying 133 = -16t2 + 96t + 5 Reorder the terms: 133 = 5 + 96t + -16t2 Solving 133 = 5 + 96t + -16t2 Solving for variable 't'. Combine like terms: 133 + -5 = 128 128 + -96t + 16t2 = 5 + 96t + -16t2 + -5 + -96t + 16t2 Reorder the terms: 128 + -96t + 16t2 = 5 + -5 + 96t + -96t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 128 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 128 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 128 + -96t + 16t2 = 0 + -16t2 + 16t2 128 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 128 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(8 + -6t + t2) = 0 Factor a trinomial. 16((2 + -1t)(4 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
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 = 4Solution
t = {2, 4}
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