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Simplifying 0 = x2 + 2xy + y2 Reorder the terms: 0 = 2xy + x2 + y2 Solving 0 = 2xy + x2 + y2 Solving for variable 'x'. Remove the zero: -2xy + -1x2 + -1y2 = 2xy + x2 + y2 + -2xy + -1x2 + -1y2 Reorder the terms: -2xy + -1x2 + -1y2 = 2xy + -2xy + x2 + -1x2 + y2 + -1y2 Combine like terms: 2xy + -2xy = 0 -2xy + -1x2 + -1y2 = 0 + x2 + -1x2 + y2 + -1y2 -2xy + -1x2 + -1y2 = x2 + -1x2 + y2 + -1y2 Combine like terms: x2 + -1x2 = 0 -2xy + -1x2 + -1y2 = 0 + y2 + -1y2 -2xy + -1x2 + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -2xy + -1x2 + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2xy + x2 + y2) = 0 Factor a trinomial. -1((x + y)(x + y)) = 0 Ignore the factor -1.Subproblem 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 + 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 = -1ySolution
x = {-1y, -1y}
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