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Simplifying 20z2 + 19z + 13 = 0 Reorder the terms: 13 + 19z + 20z2 = 0 Solving 13 + 19z + 20z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.65 + 0.95z + z2 = 0 Move the constant term to the right: Add '-0.65' to each side of the equation. 0.65 + 0.95z + -0.65 + z2 = 0 + -0.65 Reorder the terms: 0.65 + -0.65 + 0.95z + z2 = 0 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + 0.95z + z2 = 0 + -0.65 0.95z + z2 = 0 + -0.65 Combine like terms: 0 + -0.65 = -0.65 0.95z + z2 = -0.65 The z term is 0.95z. Take half its coefficient (0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. 0.95z + 0.225625 + z2 = -0.65 + 0.225625 Reorder the terms: 0.225625 + 0.95z + z2 = -0.65 + 0.225625 Combine like terms: -0.65 + 0.225625 = -0.424375 0.225625 + 0.95z + z2 = -0.424375 Factor a perfect square on the left side: (z + 0.475)(z + 0.475) = -0.424375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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