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Simplifying 4z2 + 3z + 7 = 0 Reorder the terms: 7 + 3z + 4z2 = 0 Solving 7 + 3z + 4z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 0.75z + z2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.75z + -1.75 + z2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.75z + z2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.75z + z2 = 0 + -1.75 0.75z + z2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.75z + z2 = -1.75 The z term is 0.75z. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75z + 0.140625 + z2 = -1.75 + 0.140625 Reorder the terms: 0.140625 + 0.75z + z2 = -1.75 + 0.140625 Combine like terms: -1.75 + 0.140625 = -1.609375 0.140625 + 0.75z + z2 = -1.609375 Factor a perfect square on the left side: (z + 0.375)(z + 0.375) = -1.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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