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Simplifying 2z(3z + 4) + 9 = 0 Reorder the terms: 2z(4 + 3z) + 9 = 0 (4 * 2z + 3z * 2z) + 9 = 0 (8z + 6z2) + 9 = 0 Reorder the terms: 9 + 8z + 6z2 = 0 Solving 9 + 8z + 6z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + 1.333333333z + z2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.333333333z + -1.5 + z2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.333333333z + z2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.333333333z + z2 = 0 + -1.5 1.333333333z + z2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.333333333z + z2 = -1.5 The z term is 1.333333333z. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333z + 0.4444444442 + z2 = -1.5 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333z + z2 = -1.5 + 0.4444444442 Combine like terms: -1.5 + 0.4444444442 = -1.0555555558 0.4444444442 + 1.333333333z + z2 = -1.0555555558 Factor a perfect square on the left side: (z + 0.6666666665)(z + 0.6666666665) = -1.0555555558 Can't calculate square root of the right side. The solution to this equation could not be determined.
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