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Simplifying 7 + 5z2 = -8z Solving 7 + 5z2 = -8z Solving for variable 'z'. Reorder the terms: 7 + 8z + 5z2 = -8z + 8z Combine like terms: -8z + 8z = 0 7 + 8z + 5z2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 1.6z + z2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.6z + -1.4 + z2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.6z + z2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.6z + z2 = 0 + -1.4 1.6z + z2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.6z + z2 = -1.4 The z term is 1.6z. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6z + 0.64 + z2 = -1.4 + 0.64 Reorder the terms: 0.64 + 1.6z + z2 = -1.4 + 0.64 Combine like terms: -1.4 + 0.64 = -0.76 0.64 + 1.6z + z2 = -0.76 Factor a perfect square on the left side: (z + 0.8)(z + 0.8) = -0.76 Can't calculate square root of the right side. The solution to this equation could not be determined.
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