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Simplifying 3 = -16t2 + 19t + 0 Reorder the terms: 3 = 0 + 19t + -16t2 Remove the zero: 3 = 19t + -16t2 Solving 3 = 19t + -16t2 Solving for variable 't'. Reorder the terms: 3 + -19t + 16t2 = 19t + -19t + -16t2 + 16t2 Combine like terms: 19t + -19t = 0 3 + -19t + 16t2 = 0 + -16t2 + 16t2 3 + -19t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 3 + -19t + 16t2 = 0 Factor a trinomial. (3 + -16t)(1 + -1t) = 0Subproblem 1
Set the factor '(3 + -16t)' equal to zero and attempt to solve: Simplifying 3 + -16t = 0 Solving 3 + -16t = 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 + -16t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -16t = 0 + -3 -16t = 0 + -3 Combine like terms: 0 + -3 = -3 -16t = -3 Divide each side by '-16'. t = 0.1875 Simplifying t = 0.1875Subproblem 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 = {0.1875, 1}
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