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Simplifying y4 + y2 + -5 = 0 Reorder the terms: -5 + y2 + y4 = 0 Solving -5 + y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + y2 + 5 + y4 = 0 + 5 Reorder the terms: -5 + 5 + y2 + y4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + y2 + y4 = 0 + 5 y2 + y4 = 0 + 5 Combine like terms: 0 + 5 = 5 y2 + y4 = 5 The y term is y2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y2 + 0.25 + y4 = 5 + 0.25 Reorder the terms: 0.25 + y2 + y4 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + y2 + y4 = 5.25 Factor a perfect square on the left side: (y2 + 0.5)(y2 + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (y2 + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
y2 + 0.5 = 2.291287847 Simplifying y2 + 0.5 = 2.291287847 Reorder the terms: 0.5 + y2 = 2.291287847 Solving 0.5 + y2 = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = 2.291287847 + -0.5 y2 = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 y2 = 1.791287847 Simplifying y2 = 1.791287847 Take the square root of each side: y = {-1.338390021, 1.338390021}Subproblem 2
y2 + 0.5 = -2.291287847 Simplifying y2 + 0.5 = -2.291287847 Reorder the terms: 0.5 + y2 = -2.291287847 Solving 0.5 + y2 = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y2 = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = -2.291287847 + -0.5 y2 = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 y2 = -2.791287847 Simplifying y2 = -2.791287847 Reorder the terms: 2.791287847 + y2 = -2.791287847 + 2.791287847 Combine like terms: -2.791287847 + 2.791287847 = 0.000000000 2.791287847 + 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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