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Simplifying x2 + 2xy + y2 = x + y2 Reorder the terms: 2xy + x2 + y2 = x + y2 Add '-1y2' to each side of the equation. 2xy + x2 + y2 + -1y2 = x + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 2xy + x2 + 0 = x + y2 + -1y2 2xy + x2 = x + y2 + -1y2 Combine like terms: y2 + -1y2 = 0 2xy + x2 = x + 0 2xy + x2 = x Solving 2xy + x2 = x Solving for variable 'x'. Reorder the terms: -1x + 2xy + x2 = x + -1x Combine like terms: x + -1x = 0 -1x + 2xy + x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 2y + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 2y + x)' equal to zero and attempt to solve: Simplifying -1 + 2y + x = 0 Reorder the terms: -1 + x + 2y = 0 Solving -1 + x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + x + 1 + 2y = 0 + 1 Reorder the terms: -1 + 1 + x + 2y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x + 2y = 0 + 1 x + 2y = 0 + 1 Combine like terms: 0 + 1 = 1 x + 2y = 1 Add '-2y' to each side of the equation. x + 2y + -2y = 1 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 1 + -2y x = 1 + -2y Simplifying x = 1 + -2ySolution
x = {0, 1 + -2y}
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