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Simplifying y2 + 10y + 23 = 0 Reorder the terms: 23 + 10y + y2 = 0 Solving 23 + 10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 10y + -23 + y2 = 0 + -23 Reorder the terms: 23 + -23 + 10y + y2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 10y + y2 = 0 + -23 10y + y2 = 0 + -23 Combine like terms: 0 + -23 = -23 10y + y2 = -23 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = -23 + 25 Reorder the terms: 25 + 10y + y2 = -23 + 25 Combine like terms: -23 + 25 = 2 25 + 10y + y2 = 2 Factor a perfect square on the left side: (y + 5)(y + 5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y + 5) equal to 1.414213562 and -1.414213562.Subproblem 1
y + 5 = 1.414213562 Simplifying y + 5 = 1.414213562 Reorder the terms: 5 + y = 1.414213562 Solving 5 + y = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 1.414213562 + -5 Combine like terms: 5 + -5 = 0 0 + y = 1.414213562 + -5 y = 1.414213562 + -5 Combine like terms: 1.414213562 + -5 = -3.585786438 y = -3.585786438 Simplifying y = -3.585786438Subproblem 2
y + 5 = -1.414213562 Simplifying y + 5 = -1.414213562 Reorder the terms: 5 + y = -1.414213562 Solving 5 + y = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -1.414213562 + -5 Combine like terms: 5 + -5 = 0 0 + y = -1.414213562 + -5 y = -1.414213562 + -5 Combine like terms: -1.414213562 + -5 = -6.414213562 y = -6.414213562 Simplifying y = -6.414213562Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.585786438, -6.414213562}
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