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Simplifying (2y + -1)(y + -2) = 6 Reorder the terms: (-1 + 2y)(y + -2) = 6 Reorder the terms: (-1 + 2y)(-2 + y) = 6 Multiply (-1 + 2y) * (-2 + y) (-1(-2 + y) + 2y * (-2 + y)) = 6 ((-2 * -1 + y * -1) + 2y * (-2 + y)) = 6 ((2 + -1y) + 2y * (-2 + y)) = 6 (2 + -1y + (-2 * 2y + y * 2y)) = 6 (2 + -1y + (-4y + 2y2)) = 6 Combine like terms: -1y + -4y = -5y (2 + -5y + 2y2) = 6 Solving 2 + -5y + 2y2 = 6 Solving for variable 'y'. Reorder the terms: 2 + -6 + -5y + 2y2 = 6 + -6 Combine like terms: 2 + -6 = -4 -4 + -5y + 2y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -4 + -5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -2.5y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.5y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -2.5y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.5y + y2 = 0 + 2 -2.5y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.5y + y2 = 2 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = 2 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + -2.5y + y2 = 3.5625 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (y + -1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
y + -1.25 = 1.887458609 Simplifying y + -1.25 = 1.887458609 Reorder the terms: -1.25 + y = 1.887458609 Solving -1.25 + y = 1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 1.887458609 + 1.25 y = 1.887458609 + 1.25 Combine like terms: 1.887458609 + 1.25 = 3.137458609 y = 3.137458609 Simplifying y = 3.137458609Subproblem 2
y + -1.25 = -1.887458609 Simplifying y + -1.25 = -1.887458609 Reorder the terms: -1.25 + y = -1.887458609 Solving -1.25 + y = -1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -1.887458609 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -1.887458609 + 1.25 y = -1.887458609 + 1.25 Combine like terms: -1.887458609 + 1.25 = -0.637458609 y = -0.637458609 Simplifying y = -0.637458609Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.137458609, -0.637458609}
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