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Simplifying z4 + 8z2 + 36 = 0 Reorder the terms: 36 + 8z2 + z4 = 0 Solving 36 + 8z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 8z2 + -36 + z4 = 0 + -36 Reorder the terms: 36 + -36 + 8z2 + z4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 8z2 + z4 = 0 + -36 8z2 + z4 = 0 + -36 Combine like terms: 0 + -36 = -36 8z2 + z4 = -36 The z term is 8z2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8z2 + 16 + z4 = -36 + 16 Reorder the terms: 16 + 8z2 + z4 = -36 + 16 Combine like terms: -36 + 16 = -20 16 + 8z2 + z4 = -20 Factor a perfect square on the left side: (z2 + 4)(z2 + 4) = -20 Can't calculate square root of the right side. The solution to this equation could not be determined.
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