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Simplifying 10x5y + -10xy5 = 0 Reorder the terms: -10xy5 + 10x5y = 0 Solving -10xy5 + 10x5y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10xy'. 10xy(-1y4 + x4) = 0 Factor a difference between two squares. 10xy((y2 + x2)(-1y2 + x2)) = 0 Factor a difference between two squares. 10xy((y2 + x2)((y + x)(-1y + x))) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve: Simplifying xy = 0 Solving xy = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy = 0 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 '(y2 + x2)' equal to zero and attempt to solve: Simplifying y2 + x2 = 0 Reorder the terms: 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 3
Set the factor '(y + x)' equal to zero and attempt to solve: Simplifying y + x = 0 Reorder the terms: 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 '(-1y + x)' equal to zero and attempt to solve: Simplifying -1y + x = 0 Reorder the terms: 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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