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Simplifying 7t2 + -4t = 3t2 + -1 Reorder the terms: -4t + 7t2 = 3t2 + -1 Reorder the terms: -4t + 7t2 = -1 + 3t2 Solving -4t + 7t2 = -1 + 3t2 Solving for variable 't'. Reorder the terms: 1 + -4t + 7t2 + -3t2 = -1 + 3t2 + 1 + -3t2 Combine like terms: 7t2 + -3t2 = 4t2 1 + -4t + 4t2 = -1 + 3t2 + 1 + -3t2 Reorder the terms: 1 + -4t + 4t2 = -1 + 1 + 3t2 + -3t2 Combine like terms: -1 + 1 = 0 1 + -4t + 4t2 = 0 + 3t2 + -3t2 1 + -4t + 4t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 1 + -4t + 4t2 = 0 Factor a trinomial. (1 + -2t)(1 + -2t) = 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 + -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 = {0.5, 0.5}
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