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Simplifying 2y2 + y = 404 Reorder the terms: y + 2y2 = 404 Solving y + 2y2 = 404 Solving for variable 'y'. Reorder the terms: -404 + y + 2y2 = 404 + -404 Combine like terms: 404 + -404 = 0 -404 + y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -202 + 0.5y + y2 = 0 Move the constant term to the right: Add '202' to each side of the equation. -202 + 0.5y + 202 + y2 = 0 + 202 Reorder the terms: -202 + 202 + 0.5y + y2 = 0 + 202 Combine like terms: -202 + 202 = 0 0 + 0.5y + y2 = 0 + 202 0.5y + y2 = 0 + 202 Combine like terms: 0 + 202 = 202 0.5y + y2 = 202 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5y + 0.25 + y2 = 202 + 0.25 Reorder the terms: 0.25 + 0.5y + y2 = 202 + 0.25 Combine like terms: 202 + 0.25 = 202.25 0.25 + 0.5y + y2 = 202.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (y + 0.5) equal to 14.221462653 and -14.221462653.Subproblem 1
y + 0.5 = 14.221462653 Simplifying y + 0.5 = 14.221462653 Reorder the terms: 0.5 + y = 14.221462653 Solving 0.5 + y = 14.221462653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 14.221462653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 14.221462653 + -0.5 y = 14.221462653 + -0.5 Combine like terms: 14.221462653 + -0.5 = 13.721462653 y = 13.721462653 Simplifying y = 13.721462653Subproblem 2
y + 0.5 = -14.221462653 Simplifying y + 0.5 = -14.221462653 Reorder the terms: 0.5 + y = -14.221462653 Solving 0.5 + y = -14.221462653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -14.221462653 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -14.221462653 + -0.5 y = -14.221462653 + -0.5 Combine like terms: -14.221462653 + -0.5 = -14.721462653 y = -14.721462653 Simplifying y = -14.721462653Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.721462653, -14.721462653}
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