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Simplifying y4 + 5y2 + -196 = 0 Reorder the terms: -196 + 5y2 + y4 = 0 Solving -196 + 5y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + 5y2 + 196 + y4 = 0 + 196 Reorder the terms: -196 + 196 + 5y2 + y4 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 5y2 + y4 = 0 + 196 5y2 + y4 = 0 + 196 Combine like terms: 0 + 196 = 196 5y2 + y4 = 196 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 = 196 + 6.25 Reorder the terms: 6.25 + 5y2 + y4 = 196 + 6.25 Combine like terms: 196 + 6.25 = 202.25 6.25 + 5y2 + y4 = 202.25 Factor a perfect square on the left side: (y2 + 2.5)(y2 + 2.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (y2 + 2.5) equal to 14.221462653 and -14.221462653.Subproblem 1
y2 + 2.5 = 14.221462653 Simplifying y2 + 2.5 = 14.221462653 Reorder the terms: 2.5 + y2 = 14.221462653 Solving 2.5 + y2 = 14.221462653 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 = 14.221462653 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y2 = 14.221462653 + -2.5 y2 = 14.221462653 + -2.5 Combine like terms: 14.221462653 + -2.5 = 11.721462653 y2 = 11.721462653 Simplifying y2 = 11.721462653 Take the square root of each side: y = {-3.42366217, 3.42366217}Subproblem 2
y2 + 2.5 = -14.221462653 Simplifying y2 + 2.5 = -14.221462653 Reorder the terms: 2.5 + y2 = -14.221462653 Solving 2.5 + y2 = -14.221462653 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 = -14.221462653 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y2 = -14.221462653 + -2.5 y2 = -14.221462653 + -2.5 Combine like terms: -14.221462653 + -2.5 = -16.721462653 y2 = -16.721462653 Simplifying y2 = -16.721462653 Reorder the terms: 16.721462653 + y2 = -16.721462653 + 16.721462653 Combine like terms: -16.721462653 + 16.721462653 = 0.000000000 16.721462653 + 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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