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Simplifying X2 + 2xy + y2 + 2x + 2y + 1 = 0 Reorder the terms: 1 + X2 + 2x + 2xy + 2y + y2 = 0 Solving 1 + X2 + 2x + 2xy + 2y + y2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + X2 + 2x + 2xy + 2y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + X2 + 2x + 2xy + 2y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + X2 + 2x + 2xy + 2y + y2 = 0 + -1 X2 + 2x + 2xy + 2y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 X2 + 2x + 2xy + 2y + y2 = -1 Add '-2x' to each side of the equation. X2 + 2x + 2xy + 2y + -2x + y2 = -1 + -2x Reorder the terms: X2 + 2x + -2x + 2xy + 2y + y2 = -1 + -2x Combine like terms: 2x + -2x = 0 X2 + 0 + 2xy + 2y + y2 = -1 + -2x X2 + 2xy + 2y + y2 = -1 + -2x Add '-2xy' to each side of the equation. X2 + 2xy + 2y + -2xy + y2 = -1 + -2x + -2xy Reorder the terms: X2 + 2xy + -2xy + 2y + y2 = -1 + -2x + -2xy Combine like terms: 2xy + -2xy = 0 X2 + 0 + 2y + y2 = -1 + -2x + -2xy X2 + 2y + y2 = -1 + -2x + -2xy Add '-2y' to each side of the equation. X2 + 2y + -2y + y2 = -1 + -2x + -2xy + -2y Combine like terms: 2y + -2y = 0 X2 + 0 + y2 = -1 + -2x + -2xy + -2y X2 + y2 = -1 + -2x + -2xy + -2y Add '-1y2' to each side of the equation. X2 + y2 + -1y2 = -1 + -2x + -2xy + -2y + -1y2 Combine like terms: y2 + -1y2 = 0 X2 + 0 = -1 + -2x + -2xy + -2y + -1y2 X2 = -1 + -2x + -2xy + -2y + -1y2 Simplifying X2 = -1 + -2x + -2xy + -2y + -1y2 Reorder the terms: 1 + X2 + 2x + 2xy + 2y + y2 = -1 + -2x + -2xy + -2y + -1y2 + 1 + 2x + 2xy + 2y + y2 Reorder the terms: 1 + X2 + 2x + 2xy + 2y + y2 = -1 + 1 + -2x + 2x + -2xy + 2xy + -2y + 2y + -1y2 + y2 Combine like terms: -1 + 1 = 0 1 + X2 + 2x + 2xy + 2y + y2 = 0 + -2x + 2x + -2xy + 2xy + -2y + 2y + -1y2 + y2 1 + X2 + 2x + 2xy + 2y + y2 = -2x + 2x + -2xy + 2xy + -2y + 2y + -1y2 + y2 Combine like terms: -2x + 2x = 0 1 + X2 + 2x + 2xy + 2y + y2 = 0 + -2xy + 2xy + -2y + 2y + -1y2 + y2 1 + X2 + 2x + 2xy + 2y + y2 = -2xy + 2xy + -2y + 2y + -1y2 + y2 Combine like terms: -2xy + 2xy = 0 1 + X2 + 2x + 2xy + 2y + y2 = 0 + -2y + 2y + -1y2 + y2 1 + X2 + 2x + 2xy + 2y + y2 = -2y + 2y + -1y2 + y2 Combine like terms: -2y + 2y = 0 1 + X2 + 2x + 2xy + 2y + y2 = 0 + -1y2 + y2 1 + X2 + 2x + 2xy + 2y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 1 + X2 + 2x + 2xy + 2y + y2 = 0 The solution to this equation could not be determined.
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