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Simplifying 4a4 + 3a2 + 1 = 0 Reorder the terms: 1 + 3a2 + 4a4 = 0 Solving 1 + 3a2 + 4a4 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.75a2 + a4 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.75a2 + -0.25 + a4 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.75a2 + a4 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.75a2 + a4 = 0 + -0.25 0.75a2 + a4 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.75a2 + a4 = -0.25 The a term is 0.75a2. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75a2 + 0.140625 + a4 = -0.25 + 0.140625 Reorder the terms: 0.140625 + 0.75a2 + a4 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + 0.75a2 + a4 = -0.109375 Factor a perfect square on the left side: (a2 + 0.375)(a2 + 0.375) = -0.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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