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Simplifying z2 = 3z + -18 Reorder the terms: z2 = -18 + 3z Solving z2 = -18 + 3z Solving for variable 'z'. Reorder the terms: 18 + -3z + z2 = -18 + 3z + 18 + -3z Reorder the terms: 18 + -3z + z2 = -18 + 18 + 3z + -3z Combine like terms: -18 + 18 = 0 18 + -3z + z2 = 0 + 3z + -3z 18 + -3z + z2 = 3z + -3z Combine like terms: 3z + -3z = 0 18 + -3z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -3z + -18 + z2 = 0 + -18 Reorder the terms: 18 + -18 + -3z + z2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -3z + z2 = 0 + -18 -3z + z2 = 0 + -18 Combine like terms: 0 + -18 = -18 -3z + z2 = -18 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 = -18 + 2.25 Reorder the terms: 2.25 + -3z + z2 = -18 + 2.25 Combine like terms: -18 + 2.25 = -15.75 2.25 + -3z + z2 = -15.75 Factor a perfect square on the left side: (z + -1.5)(z + -1.5) = -15.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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