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Simplifying y2 + 7y + 1 = 0 Reorder the terms: 1 + 7y + y2 = 0 Solving 1 + 7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 7y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7y + y2 = 0 + -1 7y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 7y + y2 = -1 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = -1 + 12.25 Reorder the terms: 12.25 + 7y + y2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + 7y + y2 = 11.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (y + 3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
y + 3.5 = 3.354101966 Simplifying y + 3.5 = 3.354101966 Reorder the terms: 3.5 + y = 3.354101966 Solving 3.5 + y = 3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 3.354101966 + -3.5 y = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 y = -0.145898034 Simplifying y = -0.145898034Subproblem 2
y + 3.5 = -3.354101966 Simplifying y + 3.5 = -3.354101966 Reorder the terms: 3.5 + y = -3.354101966 Solving 3.5 + y = -3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -3.354101966 + -3.5 y = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 y = -6.854101966 Simplifying y = -6.854101966Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.145898034, -6.854101966}
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