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Simplifying y4 + -4y2 + -576 = 0 Reorder the terms: -576 + -4y2 + y4 = 0 Solving -576 + -4y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + -4y2 + 576 + y4 = 0 + 576 Reorder the terms: -576 + 576 + -4y2 + y4 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + -4y2 + y4 = 0 + 576 -4y2 + y4 = 0 + 576 Combine like terms: 0 + 576 = 576 -4y2 + y4 = 576 The y term is -4y2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y2 + 4 + y4 = 576 + 4 Reorder the terms: 4 + -4y2 + y4 = 576 + 4 Combine like terms: 576 + 4 = 580 4 + -4y2 + y4 = 580 Factor a perfect square on the left side: (y2 + -2)(y2 + -2) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (y2 + -2) equal to 24.083189158 and -24.083189158.Subproblem 1
y2 + -2 = 24.083189158 Simplifying y2 + -2 = 24.083189158 Reorder the terms: -2 + y2 = 24.083189158 Solving -2 + y2 = 24.083189158 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y2 = 24.083189158 + 2 Combine like terms: -2 + 2 = 0 0 + y2 = 24.083189158 + 2 y2 = 24.083189158 + 2 Combine like terms: 24.083189158 + 2 = 26.083189158 y2 = 26.083189158 Simplifying y2 = 26.083189158 Take the square root of each side: y = {-5.107170367, 5.107170367}Subproblem 2
y2 + -2 = -24.083189158 Simplifying y2 + -2 = -24.083189158 Reorder the terms: -2 + y2 = -24.083189158 Solving -2 + y2 = -24.083189158 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y2 = -24.083189158 + 2 Combine like terms: -2 + 2 = 0 0 + y2 = -24.083189158 + 2 y2 = -24.083189158 + 2 Combine like terms: -24.083189158 + 2 = -22.083189158 y2 = -22.083189158 Simplifying y2 = -22.083189158 Reorder the terms: 22.083189158 + y2 = -22.083189158 + 22.083189158 Combine like terms: -22.083189158 + 22.083189158 = 0.000000000 22.083189158 + 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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