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Simplifying 0 = -16t2 + 10t + 9 Reorder the terms: 0 = 9 + 10t + -16t2 Solving 0 = 9 + 10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + -10t + 16t2 = 9 + 10t + -16t2 + -9 + -10t + 16t2 Reorder the terms: -9 + -10t + 16t2 = 9 + -9 + 10t + -10t + -16t2 + 16t2 Combine like terms: 9 + -9 = 0 -9 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 -9 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 -9 + -10t + 16t2 = 0 + -16t2 + 16t2 -9 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -9 + -10t + 16t2 = 0 Factor a trinomial. (-1 + -2t)(9 + -8t) = 0Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 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 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(9 + -8t)' equal to zero and attempt to solve: Simplifying 9 + -8t = 0 Solving 9 + -8t = 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 + -8t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8t = 0 + -9 -8t = 0 + -9 Combine like terms: 0 + -9 = -9 -8t = -9 Divide each side by '-8'. t = 1.125 Simplifying t = 1.125Solution
t = {-0.5, 1.125}
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