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Simplifying t2 + -5t = 18 + 2t Reorder the terms: -5t + t2 = 18 + 2t Solving -5t + t2 = 18 + 2t Solving for variable 't'. Reorder the terms: -18 + -5t + -2t + t2 = 18 + 2t + -18 + -2t Combine like terms: -5t + -2t = -7t -18 + -7t + t2 = 18 + 2t + -18 + -2t Reorder the terms: -18 + -7t + t2 = 18 + -18 + 2t + -2t Combine like terms: 18 + -18 = 0 -18 + -7t + t2 = 0 + 2t + -2t -18 + -7t + t2 = 2t + -2t Combine like terms: 2t + -2t = 0 -18 + -7t + t2 = 0 Factor a trinomial. (-2 + -1t)(9 + -1t) = 0Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-2, 9}
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