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Simplifying x4 + -2x2y2 + y4 = 0 Reorder the terms: -2x2y2 + x4 + y4 = 0 Solving -2x2y2 + x4 + y4 = 0 Solving for variable 'x'. Factor a trinomial. (x2 + -1y2)(x2 + -1y2) = 0 Factor a difference between two squares. ((x + y)(x + -1y))(x2 + -1y2) = 0 Factor a difference between two squares. ((x + y)(x + -1y))(x + y)(x + -1y) = 0Subproblem 1
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 2
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 = ySubproblem 3
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 4
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, -1y, y}
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