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Simplifying y4 + y2 = 1 Reorder the terms: y2 + y4 = 1 Solving y2 + y4 = 1 Solving for variable 'y'. Reorder the terms: -1 + y2 + y4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + y2 + 1 + y4 = 0 + 1 Reorder the terms: -1 + 1 + y2 + y4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + y2 + y4 = 0 + 1 y2 + y4 = 0 + 1 Combine like terms: 0 + 1 = 1 y2 + y4 = 1 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 = 1 + 0.25 Reorder the terms: 0.25 + y2 + y4 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + y2 + y4 = 1.25 Factor a perfect square on the left side: (y2 + 0.5)(y2 + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (y2 + 0.5) equal to 1.118033989 and -1.118033989.Subproblem 1
y2 + 0.5 = 1.118033989 Simplifying y2 + 0.5 = 1.118033989 Reorder the terms: 0.5 + y2 = 1.118033989 Solving 0.5 + y2 = 1.118033989 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 = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = 1.118033989 + -0.5 y2 = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 y2 = 0.618033989 Simplifying y2 = 0.618033989 Take the square root of each side: y = {-0.786151378, 0.786151378}Subproblem 2
y2 + 0.5 = -1.118033989 Simplifying y2 + 0.5 = -1.118033989 Reorder the terms: 0.5 + y2 = -1.118033989 Solving 0.5 + y2 = -1.118033989 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 = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y2 = -1.118033989 + -0.5 y2 = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 y2 = -1.618033989 Simplifying y2 = -1.618033989 Reorder the terms: 1.618033989 + y2 = -1.618033989 + 1.618033989 Combine like terms: -1.618033989 + 1.618033989 = 0.000000000 1.618033989 + 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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