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Simplifying z2 + 3z = -40 Reorder the terms: 3z + z2 = -40 Solving 3z + z2 = -40 Solving for variable 'z'. Reorder the terms: 40 + 3z + z2 = -40 + 40 Combine like terms: -40 + 40 = 0 40 + 3z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 3z + -40 + z2 = 0 + -40 Reorder the terms: 40 + -40 + 3z + z2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 3z + z2 = 0 + -40 3z + z2 = 0 + -40 Combine like terms: 0 + -40 = -40 3z + z2 = -40 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 = -40 + 2.25 Reorder the terms: 2.25 + 3z + z2 = -40 + 2.25 Combine like terms: -40 + 2.25 = -37.75 2.25 + 3z + z2 = -37.75 Factor a perfect square on the left side: (z + 1.5)(z + 1.5) = -37.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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