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Simplifying -5t = 2t2 + -18 Reorder the terms: -5t = -18 + 2t2 Solving -5t = -18 + 2t2 Solving for variable 't'. Reorder the terms: 18 + -5t + -2t2 = -18 + 2t2 + 18 + -2t2 Reorder the terms: 18 + -5t + -2t2 = -18 + 18 + 2t2 + -2t2 Combine like terms: -18 + 18 = 0 18 + -5t + -2t2 = 0 + 2t2 + -2t2 18 + -5t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 18 + -5t + -2t2 = 0 Factor a trinomial. (2 + -1t)(9 + 2t) = 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 + 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 = {2, -4.5}
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