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Simplifying z = 1 + z2 Solving z = 1 + z2 Solving for variable 'z'. Reorder the terms: -1 + z + -1z2 = 1 + z2 + -1 + -1z2 Reorder the terms: -1 + z + -1z2 = 1 + -1 + z2 + -1z2 Combine like terms: 1 + -1 = 0 -1 + z + -1z2 = 0 + z2 + -1z2 -1 + z + -1z2 = z2 + -1z2 Combine like terms: z2 + -1z2 = 0 -1 + z + -1z2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -1z + z2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + -1z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z + z2 = 0 + -1 -1z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1z + z2 = -1 The z term is z. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1z + 0.25 + z2 = -1 + 0.25 Reorder the terms: 0.25 + -1z + z2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1z + z2 = -0.75 Factor a perfect square on the left side: (z + 0.5)(z + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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