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Simplifying 0 = -16t2 + 38t + 5 Reorder the terms: 0 = 5 + 38t + -16t2 Solving 0 = 5 + 38t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -38t + 16t2 = 5 + 38t + -16t2 + -5 + -38t + 16t2 Reorder the terms: -5 + -38t + 16t2 = 5 + -5 + 38t + -38t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -38t + 16t2 = 0 + 38t + -38t + -16t2 + 16t2 -5 + -38t + 16t2 = 38t + -38t + -16t2 + 16t2 Combine like terms: 38t + -38t = 0 -5 + -38t + 16t2 = 0 + -16t2 + 16t2 -5 + -38t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -38t + 16t2 = 0 Factor a trinomial. (-1 + -8t)(5 + -2t) = 0Subproblem 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 '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 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 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {-0.125, 2.5}
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