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Simplifying y2 + -13y + 14 = 0 Reorder the terms: 14 + -13y + y2 = 0 Solving 14 + -13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -13y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -13y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -13y + y2 = 0 + -14 -13y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -13y + y2 = -14 The y term is -13y. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13y + 42.25 + y2 = -14 + 42.25 Reorder the terms: 42.25 + -13y + y2 = -14 + 42.25 Combine like terms: -14 + 42.25 = 28.25 42.25 + -13y + y2 = 28.25 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (y + -6.5) equal to 5.315072906 and -5.315072906.Subproblem 1
y + -6.5 = 5.315072906 Simplifying y + -6.5 = 5.315072906 Reorder the terms: -6.5 + y = 5.315072906 Solving -6.5 + y = 5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = 5.315072906 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 5.315072906 + 6.5 y = 5.315072906 + 6.5 Combine like terms: 5.315072906 + 6.5 = 11.815072906 y = 11.815072906 Simplifying y = 11.815072906Subproblem 2
y + -6.5 = -5.315072906 Simplifying y + -6.5 = -5.315072906 Reorder the terms: -6.5 + y = -5.315072906 Solving -6.5 + y = -5.315072906 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = -5.315072906 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -5.315072906 + 6.5 y = -5.315072906 + 6.5 Combine like terms: -5.315072906 + 6.5 = 1.184927094 y = 1.184927094 Simplifying y = 1.184927094Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.815072906, 1.184927094}
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