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Simplifying -16t2 + 54t = -7 Reorder the terms: 54t + -16t2 = -7 Solving 54t + -16t2 = -7 Solving for variable 't'. Reorder the terms: 7 + 54t + -16t2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 54t + -16t2 = 0 Factor a trinomial. (7 + -2t)(1 + 8t) = 0Subproblem 1
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Subproblem 2
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 = -0.125Solution
t = {3.5, -0.125}
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