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Simplifying 54 = 60t + -16t2 Solving 54 = 60t + -16t2 Solving for variable 't'. Reorder the terms: 54 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 54 + -60t + 16t2 = 0 + -16t2 + 16t2 54 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 54 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -30t + 8t2) = 0 Factor a trinomial. 2((3 + -2t)(9 + -4t)) = 0 Ignore the factor 2.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 + -4t)' equal to zero and attempt to solve: Simplifying 9 + -4t = 0 Solving 9 + -4t = 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 + -4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4t = 0 + -9 -4t = 0 + -9 Combine like terms: 0 + -9 = -9 -4t = -9 Divide each side by '-4'. t = 2.25 Simplifying t = 2.25Solution
t = {1.5, 2.25}
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