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Simplifying 4x4 + 2x2 + 1 = 0 Reorder the terms: 1 + 2x2 + 4x4 = 0 Solving 1 + 2x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.5x2 + -0.25 + x4 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.5x2 + x4 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.5x2 + x4 = 0 + -0.25 0.5x2 + x4 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.5x2 + x4 = -0.25 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = -0.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = -0.25 + 0.0625 Combine like terms: -0.25 + 0.0625 = -0.1875 0.0625 + 0.5x2 + x4 = -0.1875 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = -0.1875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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