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Simplifying 2t2 = 7t + 1 Reorder the terms: 2t2 = 1 + 7t Solving 2t2 = 1 + 7t Solving for variable 't'. Reorder the terms: -1 + -7t + 2t2 = 1 + 7t + -1 + -7t Reorder the terms: -1 + -7t + 2t2 = 1 + -1 + 7t + -7t Combine like terms: 1 + -1 = 0 -1 + -7t + 2t2 = 0 + 7t + -7t -1 + -7t + 2t2 = 7t + -7t Combine like terms: 7t + -7t = 0 -1 + -7t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -3.5t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.5t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.5t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.5t + t2 = 0 + 0.5 -3.5t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.5t + t2 = 0.5 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = 0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + -3.5t + t2 = 3.5625 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (t + -1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
t + -1.75 = 1.887458609 Simplifying t + -1.75 = 1.887458609 Reorder the terms: -1.75 + t = 1.887458609 Solving -1.75 + t = 1.887458609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 1.887458609 + 1.75 t = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 t = 3.637458609 Simplifying t = 3.637458609Subproblem 2
t + -1.75 = -1.887458609 Simplifying t + -1.75 = -1.887458609 Reorder the terms: -1.75 + t = -1.887458609 Solving -1.75 + t = -1.887458609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -1.887458609 + 1.75 t = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 t = -0.137458609 Simplifying t = -0.137458609Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.637458609, -0.137458609}
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