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Simplifying 0 = 8t2 + -5t + -13 Reorder the terms: 0 = -13 + -5t + 8t2 Solving 0 = -13 + -5t + 8t2 Solving for variable 't'. Combine like terms: 0 + 13 = 13 13 + 5t + -8t2 = -13 + -5t + 8t2 + 13 + 5t + -8t2 Reorder the terms: 13 + 5t + -8t2 = -13 + 13 + -5t + 5t + 8t2 + -8t2 Combine like terms: -13 + 13 = 0 13 + 5t + -8t2 = 0 + -5t + 5t + 8t2 + -8t2 13 + 5t + -8t2 = -5t + 5t + 8t2 + -8t2 Combine like terms: -5t + 5t = 0 13 + 5t + -8t2 = 0 + 8t2 + -8t2 13 + 5t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 13 + 5t + -8t2 = 0 Factor a trinomial. (13 + -8t)(1 + t) = 0Subproblem 1
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 = 1.625Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 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 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {1.625, -1}
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