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Simplifying 3z2 + 12z + 13 = 0 Reorder the terms: 13 + 12z + 3z2 = 0 Solving 13 + 12z + 3z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + 4z + z2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + 4z + -4.333333333 + z2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + 4z + z2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + 4z + z2 = 0 + -4.333333333 4z + z2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 4z + z2 = -4.333333333 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = -4.333333333 + 4 Reorder the terms: 4 + 4z + z2 = -4.333333333 + 4 Combine like terms: -4.333333333 + 4 = -0.333333333 4 + 4z + z2 = -0.333333333 Factor a perfect square on the left side: (z + 2)(z + 2) = -0.333333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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