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Simplifying (y2 + 2y + -1) + (y2 + -3y + -1) = 0 Reorder the terms: (-1 + 2y + y2) + (y2 + -3y + -1) = 0 Remove parenthesis around (-1 + 2y + y2) -1 + 2y + y2 + (y2 + -3y + -1) = 0 Reorder the terms: -1 + 2y + y2 + (-1 + -3y + y2) = 0 Remove parenthesis around (-1 + -3y + y2) -1 + 2y + y2 + -1 + -3y + y2 = 0 Reorder the terms: -1 + -1 + 2y + -3y + y2 + y2 = 0 Combine like terms: -1 + -1 = -2 -2 + 2y + -3y + y2 + y2 = 0 Combine like terms: 2y + -3y = -1y -2 + -1y + y2 + y2 = 0 Combine like terms: y2 + y2 = 2y2 -2 + -1y + 2y2 = 0 Solving -2 + -1y + 2y2 = 0 Solving for variable 'y'. 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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