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Simplifying 148 = -16t2 + 96t + 8 Reorder the terms: 148 = 8 + 96t + -16t2 Solving 148 = 8 + 96t + -16t2 Solving for variable 't'. Combine like terms: 148 + -8 = 140 140 + -96t + 16t2 = 8 + 96t + -16t2 + -8 + -96t + 16t2 Reorder the terms: 140 + -96t + 16t2 = 8 + -8 + 96t + -96t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 140 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 140 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 140 + -96t + 16t2 = 0 + -16t2 + 16t2 140 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 140 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -24t + 4t2) = 0 Factor a trinomial. 4((5 + -2t)(7 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 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 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {2.5, 3.5}
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