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Simplifying 33 = -16t2 + 42t + 6 Reorder the terms: 33 = 6 + 42t + -16t2 Solving 33 = 6 + 42t + -16t2 Solving for variable 't'. Combine like terms: 33 + -6 = 27 27 + -42t + 16t2 = 6 + 42t + -16t2 + -6 + -42t + 16t2 Reorder the terms: 27 + -42t + 16t2 = 6 + -6 + 42t + -42t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 27 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 27 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 27 + -42t + 16t2 = 0 + -16t2 + 16t2 27 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 27 + -42t + 16t2 = 0 Factor a trinomial. (9 + -8t)(3 + -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 '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {1.125, 1.5}
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