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Simplifying 0 = -16t2 + 50t + -6 Reorder the terms: 0 = -6 + 50t + -16t2 Solving 0 = -6 + 50t + -16t2 Solving for variable 't'. Combine like terms: 0 + 6 = 6 6 + -50t + 16t2 = -6 + 50t + -16t2 + 6 + -50t + 16t2 Reorder the terms: 6 + -50t + 16t2 = -6 + 6 + 50t + -50t + -16t2 + 16t2 Combine like terms: -6 + 6 = 0 6 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 6 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 6 + -50t + 16t2 = 0 + -16t2 + 16t2 6 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 6 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -25t + 8t2) = 0 Factor a trinomial. 2((1 + -8t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8t)' equal to zero and attempt to solve: Simplifying 1 + -8t = 0 Solving 1 + -8t = 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 + -8t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8t = 0 + -1 -8t = 0 + -1 Combine like terms: 0 + -1 = -1 -8t = -1 Divide each side by '-8'. t = 0.125 Simplifying t = 0.125Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {0.125, 3}
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