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Simplifying 5z2 + 12 = -6z Reorder the terms: 12 + 5z2 = -6z Solving 12 + 5z2 = -6z Solving for variable 'z'. Reorder the terms: 12 + 6z + 5z2 = -6z + 6z Combine like terms: -6z + 6z = 0 12 + 6z + 5z2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 1.2z + z2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 1.2z + -2.4 + z2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 1.2z + z2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 1.2z + z2 = 0 + -2.4 1.2z + z2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 1.2z + z2 = -2.4 The z term is 1.2z. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2z + 0.36 + z2 = -2.4 + 0.36 Reorder the terms: 0.36 + 1.2z + z2 = -2.4 + 0.36 Combine like terms: -2.4 + 0.36 = -2.04 0.36 + 1.2z + z2 = -2.04 Factor a perfect square on the left side: (z + 0.6)(z + 0.6) = -2.04 Can't calculate square root of the right side. The solution to this equation could not be determined.
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