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Simplifying t(2t + -1) = 1 Reorder the terms: t(-1 + 2t) = 1 (-1 * t + 2t * t) = 1 (-1t + 2t2) = 1 Solving -1t + 2t2 = 1 Solving for variable 't'. Reorder the terms: -1 + -1t + 2t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -1t + 2t2 = 0 Factor a trinomial. (-1 + -2t)(1 + -1t) = 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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-0.5, 1}
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