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Simplifying y4 + 0.5y2 + 0.0625 = 0 Reorder the terms: 0.0625 + 0.5y2 + y4 = 0 Solving 0.0625 + 0.5y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 0.5y2 + -0.0625 + y4 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 0.5y2 + y4 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 0.5y2 + y4 = 0 + -0.0625 0.5y2 + y4 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 0.5y2 + y4 = -0.0625 The y term is 0.5y2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y2 + 0.0625 + y4 = -0.0625 + 0.0625 Reorder the terms: 0.0625 + 0.5y2 + y4 = -0.0625 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0625 + 0.5y2 + y4 = 0.0000 Factor a perfect square on the left side: (y2 + 0.25)(y2 + 0.25) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (y2 + 0.25) equal to 0.0000 and 0.0000.Subproblem 1
y2 + 0.25 = 0.0000 Simplifying y2 + 0.25 = 0.0000 Reorder the terms: 0.25 + y2 = 0.0000 Solving 0.25 + y2 = 0.0000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y2 = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y2 = 0.0000 + -0.25 y2 = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 y2 = -0.25 Simplifying y2 = -0.25 Reorder the terms: 0.25 + y2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + y2 = 0.00 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y2 + 0.25 = 0.0000 Simplifying y2 + 0.25 = 0.0000 Reorder the terms: 0.25 + y2 = 0.0000 Solving 0.25 + y2 = 0.0000 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y2 = 0.0000 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y2 = 0.0000 + -0.25 y2 = 0.0000 + -0.25 Combine like terms: 0.0000 + -0.25 = -0.25 y2 = -0.25 Simplifying y2 = -0.25 Reorder the terms: 0.25 + y2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + y2 = 0.00 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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