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Simplifying (x + -1y)(x + y) = 1001 Multiply (x + -1y) * (x + y) (x(x + y) + -1y * (x + y)) = 1001 ((x * x + y * x) + -1y * (x + y)) = 1001 Reorder the terms: ((xy + x2) + -1y * (x + y)) = 1001 ((xy + x2) + -1y * (x + y)) = 1001 (xy + x2 + (x * -1y + y * -1y)) = 1001 (xy + x2 + (-1xy + -1y2)) = 1001 Reorder the terms: (xy + -1xy + x2 + -1y2) = 1001 Combine like terms: xy + -1xy = 0 (0 + x2 + -1y2) = 1001 (x2 + -1y2) = 1001 Solving x2 + -1y2 = 1001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y2' to each side of the equation. x2 + -1y2 + y2 = 1001 + y2 Combine like terms: -1y2 + y2 = 0 x2 + 0 = 1001 + y2 x2 = 1001 + y2 Simplifying x2 = 1001 + y2 Reorder the terms: -1001 + x2 + -1y2 = 1001 + y2 + -1001 + -1y2 Reorder the terms: -1001 + x2 + -1y2 = 1001 + -1001 + y2 + -1y2 Combine like terms: 1001 + -1001 = 0 -1001 + x2 + -1y2 = 0 + y2 + -1y2 -1001 + x2 + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -1001 + x2 + -1y2 = 0 The solution to this equation could not be determined.
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