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Simplifying 0 = -16t2 + 74t + 30 Reorder the terms: 0 = 30 + 74t + -16t2 Solving 0 = 30 + 74t + -16t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + -74t + 16t2 = 30 + 74t + -16t2 + -30 + -74t + 16t2 Reorder the terms: -30 + -74t + 16t2 = 30 + -30 + 74t + -74t + -16t2 + 16t2 Combine like terms: 30 + -30 = 0 -30 + -74t + 16t2 = 0 + 74t + -74t + -16t2 + 16t2 -30 + -74t + 16t2 = 74t + -74t + -16t2 + 16t2 Combine like terms: 74t + -74t = 0 -30 + -74t + 16t2 = 0 + -16t2 + 16t2 -30 + -74t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -74t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -37t + 8t2) = 0 Factor a trinomial. 2((-3 + -8t)(5 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -8t)' equal to zero and attempt to solve: Simplifying -3 + -8t = 0 Solving -3 + -8t = 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 + -8t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8t = 0 + 3 -8t = 0 + 3 Combine like terms: 0 + 3 = 3 -8t = 3 Divide each side by '-8'. t = -0.375 Simplifying t = -0.375Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-0.375, 5}
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