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Simplifying z4 + -6z2 + 18 = 0 Reorder the terms: 18 + -6z2 + z4 = 0 Solving 18 + -6z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -6z2 + -18 + z4 = 0 + -18 Reorder the terms: 18 + -18 + -6z2 + z4 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -6z2 + z4 = 0 + -18 -6z2 + z4 = 0 + -18 Combine like terms: 0 + -18 = -18 -6z2 + z4 = -18 The z term is -6z2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6z2 + 9 + z4 = -18 + 9 Reorder the terms: 9 + -6z2 + z4 = -18 + 9 Combine like terms: -18 + 9 = -9 9 + -6z2 + z4 = -9 Factor a perfect square on the left side: (z2 + -3)(z2 + -3) = -9 Can't calculate square root of the right side. The solution to this equation could not be determined.
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