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Simplifying 48 = -16t2 + 8t + 96 Reorder the terms: 48 = 96 + 8t + -16t2 Solving 48 = 96 + 8t + -16t2 Solving for variable 't'. Combine like terms: 48 + -96 = -48 -48 + -8t + 16t2 = 96 + 8t + -16t2 + -96 + -8t + 16t2 Reorder the terms: -48 + -8t + 16t2 = 96 + -96 + 8t + -8t + -16t2 + 16t2 Combine like terms: 96 + -96 = 0 -48 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -48 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -48 + -8t + 16t2 = 0 + -16t2 + 16t2 -48 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -48 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-6 + -1t + 2t2) = 0 Factor a trinomial. 8((-3 + -2t)(2 + -1t)) = 0 Ignore the factor 8.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 '(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 = 2Solution
t = {-1.5, 2}
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