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Simplifying 2z2 + 3z + 4 = 0 Reorder the terms: 4 + 3z + 2z2 = 0 Solving 4 + 3z + 2z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 1.5z + z2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.5z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + 1.5z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.5z + z2 = 0 + -2 1.5z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.5z + z2 = -2 The z term is 1.5z. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5z + 0.5625 + z2 = -2 + 0.5625 Reorder the terms: 0.5625 + 1.5z + z2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + 1.5z + z2 = -1.4375 Factor a perfect square on the left side: (z + 0.75)(z + 0.75) = -1.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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