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Simplifying (x2 + -1xy + y2)(x2 + y2 + xy) = 0 Reorder the terms: (-1xy + x2 + y2)(x2 + y2 + xy) = 0 Reorder the terms: (-1xy + x2 + y2)(xy + x2 + y2) = 0 Multiply (-1xy + x2 + y2) * (xy + x2 + y2) (-1xy * (xy + x2 + y2) + x2(xy + x2 + y2) + y2(xy + x2 + y2)) = 0 ((xy * -1xy + x2 * -1xy + y2 * -1xy) + x2(xy + x2 + y2) + y2(xy + x2 + y2)) = 0 Reorder the terms: ((-1xy3 + -1x2y2 + -1x3y) + x2(xy + x2 + y2) + y2(xy + x2 + y2)) = 0 ((-1xy3 + -1x2y2 + -1x3y) + x2(xy + x2 + y2) + y2(xy + x2 + y2)) = 0 (-1xy3 + -1x2y2 + -1x3y + (xy * x2 + x2 * x2 + y2 * x2) + y2(xy + x2 + y2)) = 0 Reorder the terms: (-1xy3 + -1x2y2 + -1x3y + (x2y2 + x3y + x4) + y2(xy + x2 + y2)) = 0 (-1xy3 + -1x2y2 + -1x3y + (x2y2 + x3y + x4) + y2(xy + x2 + y2)) = 0 (-1xy3 + -1x2y2 + -1x3y + x2y2 + x3y + x4 + (xy * y2 + x2 * y2 + y2 * y2)) = 0 (-1xy3 + -1x2y2 + -1x3y + x2y2 + x3y + x4 + (xy3 + x2y2 + y4)) = 0 Reorder the terms: (-1xy3 + xy3 + -1x2y2 + x2y2 + x2y2 + -1x3y + x3y + x4 + y4) = 0 Combine like terms: -1xy3 + xy3 = 0 (0 + -1x2y2 + x2y2 + x2y2 + -1x3y + x3y + x4 + y4) = 0 (-1x2y2 + x2y2 + x2y2 + -1x3y + x3y + x4 + y4) = 0 Combine like terms: -1x2y2 + x2y2 = 0 (0 + x2y2 + -1x3y + x3y + x4 + y4) = 0 (x2y2 + -1x3y + x3y + x4 + y4) = 0 Combine like terms: -1x3y + x3y = 0 (x2y2 + 0 + x4 + y4) = 0 (x2y2 + x4 + y4) = 0 Solving x2y2 + x4 + y4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1y4' to each side of the equation. x2y2 + x4 + y4 + -1y4 = 0 + -1y4 Combine like terms: y4 + -1y4 = 0 x2y2 + x4 + 0 = 0 + -1y4 x2y2 + x4 = 0 + -1y4 Remove the zero: x2y2 + x4 = -1y4 The x term is x2y2. Take half its coefficient (0.5y2). Square it (0.25y4) and add it to both sides. Add '0.25y4' to each side of the equation. x2y2 + x4 + 0.25y4 = -1y4 + 0.25y4 Combine like terms: -1y4 + 0.25y4 = -0.75y4 x2y2 + x4 + 0.25y4 = -0.75y4 Factor a perfect square on the left side: (x2 + 0.5y2)(x2 + 0.5y2) = -0.75y4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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