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Simplifying 14 = 5 + 25t + -16t2 Solving 14 = 5 + 25t + -16t2 Solving for variable 't'. Combine like terms: 14 + -5 = 9 9 + -25t + 16t2 = 5 + 25t + -16t2 + -5 + -25t + 16t2 Reorder the terms: 9 + -25t + 16t2 = 5 + -5 + 25t + -25t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 9 + -25t + 16t2 = 0 + 25t + -25t + -16t2 + 16t2 9 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 9 + -25t + 16t2 = 0 + -16t2 + 16t2 9 + -25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 9 + -25t + 16t2 = 0 Factor a trinomial. (9 + -16t)(1 + -1t) = 0Subproblem 1
Set the factor '(9 + -16t)' equal to zero and attempt to solve: Simplifying 9 + -16t = 0 Solving 9 + -16t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -16t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16t = 0 + -9 -16t = 0 + -9 Combine like terms: 0 + -9 = -9 -16t = -9 Divide each side by '-16'. t = 0.5625 Simplifying t = 0.5625Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0.5625, 1}
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