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Simplifying 84 = -16t2 + 90t + 3 Reorder the terms: 84 = 3 + 90t + -16t2 Solving 84 = 3 + 90t + -16t2 Solving for variable 't'. Combine like terms: 84 + -3 = 81 81 + -90t + 16t2 = 3 + 90t + -16t2 + -3 + -90t + 16t2 Reorder the terms: 81 + -90t + 16t2 = 3 + -3 + 90t + -90t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 81 + -90t + 16t2 = 0 + 90t + -90t + -16t2 + 16t2 81 + -90t + 16t2 = 90t + -90t + -16t2 + 16t2 Combine like terms: 90t + -90t = 0 81 + -90t + 16t2 = 0 + -16t2 + 16t2 81 + -90t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 81 + -90t + 16t2 = 0 Factor a trinomial. (9 + -8t)(9 + -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 '(9 + -2t)' equal to zero and attempt to solve: Simplifying 9 + -2t = 0 Solving 9 + -2t = 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 + -2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2t = 0 + -9 -2t = 0 + -9 Combine like terms: 0 + -9 = -9 -2t = -9 Divide each side by '-2'. t = 4.5 Simplifying t = 4.5Solution
t = {1.125, 4.5}
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