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Simplifying 2u2 + u + 2 = 0 Reorder the terms: 2 + u + 2u2 = 0 Solving 2 + u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 0.5u + u2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.5u + -1 + u2 = 0 + -1 Reorder the terms: 1 + -1 + 0.5u + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.5u + u2 = 0 + -1 0.5u + u2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.5u + u2 = -1 The u term is u. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5u + 0.25 + u2 = -1 + 0.25 Reorder the terms: 0.25 + 0.5u + u2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.5u + u2 = -0.75 Factor a perfect square on the left side: (u + 0.5)(u + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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