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Simplifying 0 = -16t2 + 8t + -1 Reorder the terms: 0 = -1 + 8t + -16t2 Solving 0 = -1 + 8t + -16t2 Solving for variable 't'. Combine like terms: 0 + 1 = 1 1 + -8t + 16t2 = -1 + 8t + -16t2 + 1 + -8t + 16t2 Reorder the terms: 1 + -8t + 16t2 = -1 + 1 + 8t + -8t + -16t2 + 16t2 Combine like terms: -1 + 1 = 0 1 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 1 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 1 + -8t + 16t2 = 0 + -16t2 + 16t2 1 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 1 + -8t + 16t2 = 0 Factor a trinomial. (1 + -4t)(1 + -4t) = 0Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 2
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Solution
t = {0.25, 0.25}
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