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Simplifying xy = x2 + 2y2 Solving xy = x2 + 2y2 Solving for variable 'x'. Reorder the terms: xy + -1x2 + -2y2 = x2 + -1x2 + 2y2 + -2y2 Combine like terms: x2 + -1x2 = 0 xy + -1x2 + -2y2 = 0 + 2y2 + -2y2 xy + -1x2 + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 xy + -1x2 + -2y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1xy + x2 + 2y2 = 0 Move the constant term to the right: Add '-2y2' to each side of the equation. -1xy + x2 + 2y2 + -2y2 = 0 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -1xy + x2 + 0 = 0 + -2y2 -1xy + x2 = 0 + -2y2 Remove the zero: -1xy + x2 = -2y2 The x term is xy. Take half its coefficient (0.5y). Square it (0.25y2) and add it to both sides. Add '0.25y2' to each side of the equation. -1xy + x2 + 0.25y2 = -2y2 + 0.25y2 Combine like terms: -2y2 + 0.25y2 = -1.75y2 -1xy + x2 + 0.25y2 = -1.75y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -1.75y2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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