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Simplifying 2z2 + -3z + 18 = 8 Reorder the terms: 18 + -3z + 2z2 = 8 Solving 18 + -3z + 2z2 = 8 Solving for variable 'z'. Reorder the terms: 18 + -8 + -3z + 2z2 = 8 + -8 Combine like terms: 18 + -8 = 10 10 + -3z + 2z2 = 8 + -8 Combine like terms: 8 + -8 = 0 10 + -3z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + -1.5z + z2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -1.5z + -5 + z2 = 0 + -5 Reorder the terms: 5 + -5 + -1.5z + z2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1.5z + z2 = 0 + -5 -1.5z + z2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1.5z + z2 = -5 The z term is -1.5z. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5z + 0.5625 + z2 = -5 + 0.5625 Reorder the terms: 0.5625 + -1.5z + z2 = -5 + 0.5625 Combine like terms: -5 + 0.5625 = -4.4375 0.5625 + -1.5z + z2 = -4.4375 Factor a perfect square on the left side: (z + -0.75)(z + -0.75) = -4.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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