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Simplifying 9z2 + 3z + 2 = 0 Reorder the terms: 2 + 3z + 9z2 = 0 Solving 2 + 3z + 9z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 0.3333333333z + z2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.3333333333z + -0.2222222222 + z2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.3333333333z + z2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.3333333333z + z2 = 0 + -0.2222222222 0.3333333333z + z2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.3333333333z + z2 = -0.2222222222 The z term is 0.3333333333z. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333z + 0.02777777779 + z2 = -0.2222222222 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333z + z2 = -0.2222222222 + 0.02777777779 Combine like terms: -0.2222222222 + 0.02777777779 = -0.19444444441 0.02777777779 + 0.3333333333z + z2 = -0.19444444441 Factor a perfect square on the left side: (z + 0.1666666667)(z + 0.1666666667) = -0.19444444441 Can't calculate square root of the right side. The solution to this equation could not be determined.
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