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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 = 6.414213562 y = 6.414213562 Simplifying y = 6.414213562Subproblem 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 = 3.585786438 y = 3.585786438 Simplifying y = 3.585786438Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.414213562, 3.585786438}
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