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Simplifying 8 + 2z2 = -5z Solving 8 + 2z2 = -5z Solving for variable 'z'. Reorder the terms: 8 + 5z + 2z2 = -5z + 5z Combine like terms: -5z + 5z = 0 8 + 5z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 2.5z + z2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 2.5z + -4 + z2 = 0 + -4 Reorder the terms: 4 + -4 + 2.5z + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2.5z + z2 = 0 + -4 2.5z + z2 = 0 + -4 Combine like terms: 0 + -4 = -4 2.5z + z2 = -4 The z term is 2.5z. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5z + 1.5625 + z2 = -4 + 1.5625 Reorder the terms: 1.5625 + 2.5z + z2 = -4 + 1.5625 Combine like terms: -4 + 1.5625 = -2.4375 1.5625 + 2.5z + z2 = -2.4375 Factor a perfect square on the left side: (z + 1.25)(z + 1.25) = -2.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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