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Simplifying -16t2 + 10t + 25 = 16 Reorder the terms: 25 + 10t + -16t2 = 16 Solving 25 + 10t + -16t2 = 16 Solving for variable 't'. Reorder the terms: 25 + -16 + 10t + -16t2 = 16 + -16 Combine like terms: 25 + -16 = 9 9 + 10t + -16t2 = 16 + -16 Combine like terms: 16 + -16 = 0 9 + 10t + -16t2 = 0 Factor a trinomial. (9 + -8t)(1 + 2t) = 0Subproblem 1
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 = 1.125Subproblem 2
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 = -0.5Solution
t = {1.125, -0.5}
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