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Simplifying z8 + 4z4 + 5 = 0 Reorder the terms: 5 + 4z4 + z8 = 0 Solving 5 + 4z4 + z8 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4z4 + -5 + z8 = 0 + -5 Reorder the terms: 5 + -5 + 4z4 + z8 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z4 + z8 = 0 + -5 4z4 + z8 = 0 + -5 Combine like terms: 0 + -5 = -5 4z4 + z8 = -5 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 = -5 + 4 Reorder the terms: 4 + 4z4 + z8 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4z4 + z8 = -1 Factor a perfect square on the left side: (z4 + 2)(z4 + 2) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined.
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