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Simplifying y2 + -13y + 24 = 0 Reorder the terms: 24 + -13y + y2 = 0 Solving 24 + -13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -13y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + -13y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -13y + y2 = 0 + -24 -13y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -13y + y2 = -24 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 = -24 + 42.25 Reorder the terms: 42.25 + -13y + y2 = -24 + 42.25 Combine like terms: -24 + 42.25 = 18.25 42.25 + -13y + y2 = 18.25 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + -6.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + -6.5 = 4.272001873 Simplifying y + -6.5 = 4.272001873 Reorder the terms: -6.5 + y = 4.272001873 Solving -6.5 + y = 4.272001873 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 = 4.272001873 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 4.272001873 + 6.5 y = 4.272001873 + 6.5 Combine like terms: 4.272001873 + 6.5 = 10.772001873 y = 10.772001873 Simplifying y = 10.772001873Subproblem 2
y + -6.5 = -4.272001873 Simplifying y + -6.5 = -4.272001873 Reorder the terms: -6.5 + y = -4.272001873 Solving -6.5 + y = -4.272001873 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 = -4.272001873 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -4.272001873 + 6.5 y = -4.272001873 + 6.5 Combine like terms: -4.272001873 + 6.5 = 2.227998127 y = 2.227998127 Simplifying y = 2.227998127Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.772001873, 2.227998127}
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