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Simplifying z4 + 2z2 + 4 = 0 Reorder the terms: 4 + 2z2 + z4 = 0 Solving 4 + 2z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2z2 + -4 + z4 = 0 + -4 Reorder the terms: 4 + -4 + 2z2 + z4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2z2 + z4 = 0 + -4 2z2 + z4 = 0 + -4 Combine like terms: 0 + -4 = -4 2z2 + z4 = -4 The z term is 2z2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2z2 + 1 + z4 = -4 + 1 Reorder the terms: 1 + 2z2 + z4 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + 2z2 + z4 = -3 Factor a perfect square on the left side: (z2 + 1)(z2 + 1) = -3 Can't calculate square root of the right side. The solution to this equation could not be determined.
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