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Simplifying 16z4 + 4z2 + 1 = 0 Reorder the terms: 1 + 4z2 + 16z4 = 0 Solving 1 + 4z2 + 16z4 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + 0.25z2 + z4 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 0.25z2 + -0.0625 + z4 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 0.25z2 + z4 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 0.25z2 + z4 = 0 + -0.0625 0.25z2 + z4 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 0.25z2 + z4 = -0.0625 The z term is 0.25z2. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25z2 + 0.015625 + z4 = -0.0625 + 0.015625 Reorder the terms: 0.015625 + 0.25z2 + z4 = -0.0625 + 0.015625 Combine like terms: -0.0625 + 0.015625 = -0.046875 0.015625 + 0.25z2 + z4 = -0.046875 Factor a perfect square on the left side: (z2 + 0.125)(z2 + 0.125) = -0.046875 Can't calculate square root of the right side. The solution to this equation could not be determined.
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