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Simplifying z8 + 4z4 + 16 = 0 Reorder the terms: 16 + 4z4 + z8 = 0 Solving 16 + 4z4 + z8 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 4z4 + -16 + z8 = 0 + -16 Reorder the terms: 16 + -16 + 4z4 + z8 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4z4 + z8 = 0 + -16 4z4 + z8 = 0 + -16 Combine like terms: 0 + -16 = -16 4z4 + z8 = -16 The z term is 4z4. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z4 + 4 + z8 = -16 + 4 Reorder the terms: 4 + 4z4 + z8 = -16 + 4 Combine like terms: -16 + 4 = -12 4 + 4z4 + z8 = -12 Factor a perfect square on the left side: (z4 + 2)(z4 + 2) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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