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Simplifying z2 + 3z + 8.5 = 0 Reorder the terms: 8.5 + 3z + z2 = 0 Solving 8.5 + 3z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + 3z + -8.5 + z2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + 3z + z2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + 3z + z2 = 0 + -8.5 3z + z2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 3z + z2 = -8.5 The z term is 3z. 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. 3z + 2.25 + z2 = -8.5 + 2.25 Reorder the terms: 2.25 + 3z + z2 = -8.5 + 2.25 Combine like terms: -8.5 + 2.25 = -6.25 2.25 + 3z + z2 = -6.25 Factor a perfect square on the left side: (z + 1.5)(z + 1.5) = -6.25 Can't calculate square root of the right side. The solution to this equation could not be determined.
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