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Simplifying y2 + 2y + -252 = 0 Reorder the terms: -252 + 2y + y2 = 0 Solving -252 + 2y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '252' to each side of the equation. -252 + 2y + 252 + y2 = 0 + 252 Reorder the terms: -252 + 252 + 2y + y2 = 0 + 252 Combine like terms: -252 + 252 = 0 0 + 2y + y2 = 0 + 252 2y + y2 = 0 + 252 Combine like terms: 0 + 252 = 252 2y + y2 = 252 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 252 + 1 Reorder the terms: 1 + 2y + y2 = 252 + 1 Combine like terms: 252 + 1 = 253 1 + 2y + y2 = 253 Factor a perfect square on the left side: (y + 1)(y + 1) = 253 Calculate the square root of the right side: 15.905973721 Break this problem into two subproblems by setting (y + 1) equal to 15.905973721 and -15.905973721.Subproblem 1
y + 1 = 15.905973721 Simplifying y + 1 = 15.905973721 Reorder the terms: 1 + y = 15.905973721 Solving 1 + y = 15.905973721 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 15.905973721 + -1 Combine like terms: 1 + -1 = 0 0 + y = 15.905973721 + -1 y = 15.905973721 + -1 Combine like terms: 15.905973721 + -1 = 14.905973721 y = 14.905973721 Simplifying y = 14.905973721Subproblem 2
y + 1 = -15.905973721 Simplifying y + 1 = -15.905973721 Reorder the terms: 1 + y = -15.905973721 Solving 1 + y = -15.905973721 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -15.905973721 + -1 Combine like terms: 1 + -1 = 0 0 + y = -15.905973721 + -1 y = -15.905973721 + -1 Combine like terms: -15.905973721 + -1 = -16.905973721 y = -16.905973721 Simplifying y = -16.905973721Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.905973721, -16.905973721}
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