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Simplifying y2 + -13y + 13 = 0 Reorder the terms: 13 + -13y + y2 = 0 Solving 13 + -13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -13y + -13 + y2 = 0 + -13 Reorder the terms: 13 + -13 + -13y + y2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -13y + y2 = 0 + -13 -13y + y2 = 0 + -13 Combine like terms: 0 + -13 = -13 -13y + y2 = -13 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 = -13 + 42.25 Reorder the terms: 42.25 + -13y + y2 = -13 + 42.25 Combine like terms: -13 + 42.25 = 29.25 42.25 + -13y + y2 = 29.25 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (y + -6.5) equal to 5.408326913 and -5.408326913.Subproblem 1
y + -6.5 = 5.408326913 Simplifying y + -6.5 = 5.408326913 Reorder the terms: -6.5 + y = 5.408326913 Solving -6.5 + y = 5.408326913 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 = 5.408326913 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 5.408326913 + 6.5 y = 5.408326913 + 6.5 Combine like terms: 5.408326913 + 6.5 = 11.908326913 y = 11.908326913 Simplifying y = 11.908326913Subproblem 2
y + -6.5 = -5.408326913 Simplifying y + -6.5 = -5.408326913 Reorder the terms: -6.5 + y = -5.408326913 Solving -6.5 + y = -5.408326913 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 = -5.408326913 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -5.408326913 + 6.5 y = -5.408326913 + 6.5 Combine like terms: -5.408326913 + 6.5 = 1.091673087 y = 1.091673087 Simplifying y = 1.091673087Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.908326913, 1.091673087}
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