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Simplifying 8t2 = 3 + -2t Solving 8t2 = 3 + -2t Solving for variable 't'. Reorder the terms: -3 + 2t + 8t2 = 3 + -2t + -3 + 2t Reorder the terms: -3 + 2t + 8t2 = 3 + -3 + -2t + 2t Combine like terms: 3 + -3 = 0 -3 + 2t + 8t2 = 0 + -2t + 2t -3 + 2t + 8t2 = -2t + 2t Combine like terms: -2t + 2t = 0 -3 + 2t + 8t2 = 0 Factor a trinomial. (-3 + -4t)(1 + -2t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
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 = 0.5Solution
t = {-0.75, 0.5}
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