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Simplifying 116 = 8 + 96t + -16(t2) Solving 116 = 8 + 96t + -16t2 Solving for variable 't'. Combine like terms: 116 + -8 = 108 108 + -96t + 16t2 = 8 + 96t + -16t2 + -8 + -96t + 16t2 Reorder the terms: 108 + -96t + 16t2 = 8 + -8 + 96t + -96t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 108 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 108 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 108 + -96t + 16t2 = 0 + -16t2 + 16t2 108 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 108 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(27 + -24t + 4t2) = 0 Factor a trinomial. 4((3 + -2t)(9 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Subproblem 2
Set the factor '(9 + -2t)' equal to zero and attempt to solve: Simplifying 9 + -2t = 0 Solving 9 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2t = 0 + -9 -2t = 0 + -9 Combine like terms: 0 + -9 = -9 -2t = -9 Divide each side by '-2'. t = 4.5 Simplifying t = 4.5Solution
t = {1.5, 4.5}
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