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Simplifying u4 + u2v2 + v4 = 0 Reorder the terms: u2v2 + u4 + v4 = 0 Solving u2v2 + u4 + v4 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-1v4' to each side of the equation. u2v2 + u4 + v4 + -1v4 = 0 + -1v4 Combine like terms: v4 + -1v4 = 0 u2v2 + u4 + 0 = 0 + -1v4 u2v2 + u4 = 0 + -1v4 Remove the zero: u2v2 + u4 = -1v4 The u term is u2v2. Take half its coefficient (0.5v2). Square it (0.25v4) and add it to both sides. Add '0.25v4' to each side of the equation. u2v2 + u4 + 0.25v4 = -1v4 + 0.25v4 Combine like terms: -1v4 + 0.25v4 = -0.75v4 u2v2 + u4 + 0.25v4 = -0.75v4 Factor a perfect square on the left side: (u2 + 0.5v2)(u2 + 0.5v2) = -0.75v4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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