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Simplifying -2y(y + -1) + -1y = -2 Reorder the terms: -2y(-1 + y) + -1y = -2 (-1 * -2y + y * -2y) + -1y = -2 (2y + -2y2) + -1y = -2 Reorder the terms: 2y + -1y + -2y2 = -2 Combine like terms: 2y + -1y = 1y 1y + -2y2 = -2 Solving 1y + -2y2 = -2 Solving for variable 'y'. Reorder the terms: 2 + 1y + -2y2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 1y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -0.5y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5y + y2 = 0 + 1 -0.5y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5y + y2 = 1 The y term is -0.5y. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5y + 0.0625 + y2 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5y + y2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5y + y2 = 1.0625 Factor a perfect square on the left side: (y + -0.25)(y + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (y + -0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
y + -0.25 = 1.030776406 Simplifying y + -0.25 = 1.030776406 Reorder the terms: -0.25 + y = 1.030776406 Solving -0.25 + y = 1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = 1.030776406 + 0.25 y = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 y = 1.280776406 Simplifying y = 1.280776406Subproblem 2
y + -0.25 = -1.030776406 Simplifying y + -0.25 = -1.030776406 Reorder the terms: -0.25 + y = -1.030776406 Solving -0.25 + y = -1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + y = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + y = -1.030776406 + 0.25 y = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 y = -0.780776406 Simplifying y = -0.780776406Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.280776406, -0.780776406}
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