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Simplifying 24 = -16t2 + 24t + 16 Reorder the terms: 24 = 16 + 24t + -16t2 Solving 24 = 16 + 24t + -16t2 Solving for variable 't'. Combine like terms: 24 + -16 = 8 8 + -24t + 16t2 = 16 + 24t + -16t2 + -16 + -24t + 16t2 Reorder the terms: 8 + -24t + 16t2 = 16 + -16 + 24t + -24t + -16t2 + 16t2 Combine like terms: 16 + -16 = 0 8 + -24t + 16t2 = 0 + 24t + -24t + -16t2 + 16t2 8 + -24t + 16t2 = 24t + -24t + -16t2 + 16t2 Combine like terms: 24t + -24t = 0 8 + -24t + 16t2 = 0 + -16t2 + 16t2 8 + -24t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 8 + -24t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + -3t + 2t2) = 0 Factor a trinomial. 8((1 + -2t)(1 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0.5, 1}
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