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Simplifying (8t2 + -10t + 2) + -1(8t + 13) = 0 Reorder the terms: (2 + -10t + 8t2) + -1(8t + 13) = 0 Remove parenthesis around (2 + -10t + 8t2) 2 + -10t + 8t2 + -1(8t + 13) = 0 Reorder the terms: 2 + -10t + 8t2 + -1(13 + 8t) = 0 2 + -10t + 8t2 + (13 * -1 + 8t * -1) = 0 2 + -10t + 8t2 + (-13 + -8t) = 0 Reorder the terms: 2 + -13 + -10t + -8t + 8t2 = 0 Combine like terms: 2 + -13 = -11 -11 + -10t + -8t + 8t2 = 0 Combine like terms: -10t + -8t = -18t -11 + -18t + 8t2 = 0 Solving -11 + -18t + 8t2 = 0 Solving for variable 't'. Factor a trinomial. (-1 + -2t)(11 + -4t) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(11 + -4t)' equal to zero and attempt to solve: Simplifying 11 + -4t = 0 Solving 11 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4t = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4t = 0 + -11 -4t = 0 + -11 Combine like terms: 0 + -11 = -11 -4t = -11 Divide each side by '-4'. t = 2.75 Simplifying t = 2.75Solution
t = {-0.5, 2.75}
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