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Simplifying z4 + -3z2 + 9 = 0 Reorder the terms: 9 + -3z2 + z4 = 0 Solving 9 + -3z2 + z4 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -3z2 + -9 + z4 = 0 + -9 Reorder the terms: 9 + -9 + -3z2 + z4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -3z2 + z4 = 0 + -9 -3z2 + z4 = 0 + -9 Combine like terms: 0 + -9 = -9 -3z2 + z4 = -9 The z term is -3z2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3z2 + 2.25 + z4 = -9 + 2.25 Reorder the terms: 2.25 + -3z2 + z4 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + -3z2 + z4 = -6.75 Factor a perfect square on the left side: (z2 + -1.5)(z2 + -1.5) = -6.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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