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Simplifying -16t2 + 24t + 60 = 68 Reorder the terms: 60 + 24t + -16t2 = 68 Solving 60 + 24t + -16t2 = 68 Solving for variable 't'. Reorder the terms: 60 + -68 + 24t + -16t2 = 68 + -68 Combine like terms: 60 + -68 = -8 -8 + 24t + -16t2 = 68 + -68 Combine like terms: 68 + -68 = 0 -8 + 24t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-1 + 3t + -2t2) = 0 Factor a trinomial. 8((-1 + t)(1 + -2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + t)' equal to zero and attempt to solve: Simplifying -1 + t = 0 Solving -1 + t = 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 + t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0 + 1 t = 0 + 1 Combine like terms: 0 + 1 = 1 t = 1 Simplifying t = 1Subproblem 2
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 = 0.5Solution
t = {1, 0.5}
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