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Simplifying 54 = -16t2 + 70t Reorder the terms: 54 = 70t + -16t2 Solving 54 = 70t + -16t2 Solving for variable 't'. Reorder the terms: 54 + -70t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 54 + -70t + 16t2 = 0 + -16t2 + 16t2 54 + -70t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 54 + -70t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -35t + 8t2) = 0 Factor a trinomial. 2((1 + -1t)(27 + -8t)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(27 + -8t)' equal to zero and attempt to solve: Simplifying 27 + -8t = 0 Solving 27 + -8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -8t = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -8t = 0 + -27 -8t = 0 + -27 Combine like terms: 0 + -27 = -27 -8t = -27 Divide each side by '-8'. t = 3.375 Simplifying t = 3.375Solution
t = {1, 3.375}
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