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Simplifying y4 + -5y2 + -12 = 0 Reorder the terms: -12 + -5y2 + y4 = 0 Solving -12 + -5y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -5y2 + 12 + y4 = 0 + 12 Reorder the terms: -12 + 12 + -5y2 + y4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5y2 + y4 = 0 + 12 -5y2 + y4 = 0 + 12 Combine like terms: 0 + 12 = 12 -5y2 + y4 = 12 The y term is -5y2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y2 + 6.25 + y4 = 12 + 6.25 Reorder the terms: 6.25 + -5y2 + y4 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5y2 + y4 = 18.25 Factor a perfect square on the left side: (y2 + -2.5)(y2 + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y2 + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y2 + -2.5 = 4.272001873 Simplifying y2 + -2.5 = 4.272001873 Reorder the terms: -2.5 + y2 = 4.272001873 Solving -2.5 + y2 = 4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y2 = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y2 = 4.272001873 + 2.5 y2 = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 y2 = 6.772001873 Simplifying y2 = 6.772001873 Take the square root of each side: y = {-2.602307029, 2.602307029}Subproblem 2
y2 + -2.5 = -4.272001873 Simplifying y2 + -2.5 = -4.272001873 Reorder the terms: -2.5 + y2 = -4.272001873 Solving -2.5 + y2 = -4.272001873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y2 = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y2 = -4.272001873 + 2.5 y2 = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 y2 = -1.772001873 Simplifying y2 = -1.772001873 Reorder the terms: 1.772001873 + y2 = -1.772001873 + 1.772001873 Combine like terms: -1.772001873 + 1.772001873 = 0.000000000 1.772001873 + y2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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