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Simplifying 5Z2 + -5Z + 4 + -1Z(3Z + -4) = 0 Reorder the terms: 5Z2 + -5Z + 4 + -1Z(-4 + 3Z) = 0 5Z2 + -5Z + 4 + (-4 * -1Z + 3Z * -1Z) = 0 5Z2 + -5Z + 4 + (4Z + -3Z2) = 0 Reorder the terms: 4 + -5Z + 4Z + 5Z2 + -3Z2 = 0 Combine like terms: -5Z + 4Z = -1Z 4 + -1Z + 5Z2 + -3Z2 = 0 Combine like terms: 5Z2 + -3Z2 = 2Z2 4 + -1Z + 2Z2 = 0 Solving 4 + -1Z + 2Z2 = 0 Solving for variable 'Z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -0.5Z + Z2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5Z + -2 + Z2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5Z + Z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5Z + Z2 = 0 + -2 -0.5Z + Z2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5Z + Z2 = -2 The Z term is -0.5Z. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5Z + 0.0625 + Z2 = -2 + 0.0625 Reorder the terms: 0.0625 + -0.5Z + Z2 = -2 + 0.0625 Combine like terms: -2 + 0.0625 = -1.9375 0.0625 + -0.5Z + Z2 = -1.9375 Factor a perfect square on the left side: (Z + -0.25)(Z + -0.25) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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