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Simplifying 2t2 = 5t + 3 Reorder the terms: 2t2 = 3 + 5t Solving 2t2 = 3 + 5t Solving for variable 't'. Reorder the terms: -3 + -5t + 2t2 = 3 + 5t + -3 + -5t Reorder the terms: -3 + -5t + 2t2 = 3 + -3 + 5t + -5t Combine like terms: 3 + -3 = 0 -3 + -5t + 2t2 = 0 + 5t + -5t -3 + -5t + 2t2 = 5t + -5t Combine like terms: 5t + -5t = 0 -3 + -5t + 2t2 = 0 Factor a trinomial. (-1 + -2t)(3 + -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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.5, 3}
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