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Simplifying z8 + 16z4 + 256 = 0 Reorder the terms: 256 + 16z4 + z8 = 0 Solving 256 + 16z4 + z8 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + 16z4 + -256 + z8 = 0 + -256 Reorder the terms: 256 + -256 + 16z4 + z8 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + 16z4 + z8 = 0 + -256 16z4 + z8 = 0 + -256 Combine like terms: 0 + -256 = -256 16z4 + z8 = -256 The z term is 16z4. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16z4 + 64 + z8 = -256 + 64 Reorder the terms: 64 + 16z4 + z8 = -256 + 64 Combine like terms: -256 + 64 = -192 64 + 16z4 + z8 = -192 Factor a perfect square on the left side: (z4 + 8)(z4 + 8) = -192 Can't calculate square root of the right side. The solution to this equation could not be determined.
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