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Simplifying (x2 + y2)(x2 + -1y2) = 0 Multiply (x2 + y2) * (x2 + -1y2) (x2(x2 + -1y2) + y2(x2 + -1y2)) = 0 ((x2 * x2 + -1y2 * x2) + y2(x2 + -1y2)) = 0 Reorder the terms: ((-1x2y2 + x4) + y2(x2 + -1y2)) = 0 ((-1x2y2 + x4) + y2(x2 + -1y2)) = 0 (-1x2y2 + x4 + (x2 * y2 + -1y2 * y2)) = 0 (-1x2y2 + x4 + (x2y2 + -1y4)) = 0 Reorder the terms: (-1x2y2 + x2y2 + x4 + -1y4) = 0 Combine like terms: -1x2y2 + x2y2 = 0 (0 + x4 + -1y4) = 0 (x4 + -1y4) = 0 Solving x4 + -1y4 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y4' to each side of the equation. x4 + -1y4 + y4 = 0 + y4 Combine like terms: -1y4 + y4 = 0 x4 + 0 = 0 + y4 x4 = 0 + y4 Remove the zero: x4 = y4 Simplifying x4 = y4 Combine like terms: y4 + -1y4 = 0 x4 + -1y4 = 0 Factor a difference between two squares. (x2 + y2)(x2 + -1y2) = 0 Factor a difference between two squares. (x2 + y2)((x + y)(x + -1y)) = 0Subproblem 1
Set the factor '(x2 + y2)' equal to zero and attempt to solve: Simplifying x2 + y2 = 0 Solving x2 + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. x2 + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 x2 + 0 = 0 + -1y2 x2 = 0 + -1y2 Remove the zero: x2 = -1y2 Simplifying x2 = -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySubproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySolution
x = {-1y, y}
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