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Simplifying 5x2 + xy + 4y2 = 0 Reorder the terms: xy + 5x2 + 4y2 = 0 Solving xy + 5x2 + 4y2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2xy + x2 + 0.8y2 = 0 Move the constant term to the right: Add '-0.8y2' to each side of the equation. 0.2xy + x2 + 0.8y2 + -0.8y2 = 0 + -0.8y2 Combine like terms: 0.8y2 + -0.8y2 = 0.0 0.2xy + x2 + 0.0 = 0 + -0.8y2 0.2xy + x2 = 0 + -0.8y2 Remove the zero: 0.2xy + x2 = -0.8y2 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. 0.2xy + x2 + 0.25y2 = -0.8y2 + 0.25y2 Combine like terms: -0.8y2 + 0.25y2 = -0.55y2 0.2xy + x2 + 0.25y2 = -0.55y2 Factor a perfect square on the left side: (x + 0.5y)(x + 0.5y) = -0.55y2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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