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Simplifying 5z2 + 4z + 12 = 0 Reorder the terms: 12 + 4z + 5z2 = 0 Solving 12 + 4z + 5z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 0.8z + z2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 0.8z + -2.4 + z2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 0.8z + z2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 0.8z + z2 = 0 + -2.4 0.8z + z2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 0.8z + z2 = -2.4 The z term is 0.8z. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8z + 0.16 + z2 = -2.4 + 0.16 Reorder the terms: 0.16 + 0.8z + z2 = -2.4 + 0.16 Combine like terms: -2.4 + 0.16 = -2.24 0.16 + 0.8z + z2 = -2.24 Factor a perfect square on the left side: (z + 0.4)(z + 0.4) = -2.24 Can't calculate square root of the right side. The solution to this equation could not be determined.
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