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Simplifying -16t2 + -2t + 409 = 370 Reorder the terms: 409 + -2t + -16t2 = 370 Solving 409 + -2t + -16t2 = 370 Solving for variable 't'. Reorder the terms: 409 + -370 + -2t + -16t2 = 370 + -370 Combine like terms: 409 + -370 = 39 39 + -2t + -16t2 = 370 + -370 Combine like terms: 370 + -370 = 0 39 + -2t + -16t2 = 0 Factor a trinomial. (3 + -2t)(13 + 8t) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(13 + 8t)' equal to zero and attempt to solve: Simplifying 13 + 8t = 0 Solving 13 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 8t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 8t = 0 + -13 8t = 0 + -13 Combine like terms: 0 + -13 = -13 8t = -13 Divide each side by '8'. t = -1.625 Simplifying t = -1.625Solution
t = {1.5, -1.625}
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