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Simplifying X2 + Y2 + 2 = 0 Reorder the terms: 2 + X2 + Y2 = 0 Solving 2 + X2 + Y2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + X2 + -2 + Y2 = 0 + -2 Reorder the terms: 2 + -2 + X2 + Y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + X2 + Y2 = 0 + -2 X2 + Y2 = 0 + -2 Combine like terms: 0 + -2 = -2 X2 + Y2 = -2 Add '-1Y2' to each side of the equation. X2 + Y2 + -1Y2 = -2 + -1Y2 Combine like terms: Y2 + -1Y2 = 0 X2 + 0 = -2 + -1Y2 X2 = -2 + -1Y2 Simplifying X2 = -2 + -1Y2 Reorder the terms: 2 + X2 + Y2 = -2 + -1Y2 + 2 + Y2 Reorder the terms: 2 + X2 + Y2 = -2 + 2 + -1Y2 + Y2 Combine like terms: -2 + 2 = 0 2 + X2 + Y2 = 0 + -1Y2 + Y2 2 + X2 + Y2 = -1Y2 + Y2 Combine like terms: -1Y2 + Y2 = 0 2 + X2 + Y2 = 0 Factor a trinomial. (X + Y)(X + Y) = 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 + 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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