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Simplifying 4n2 + 3n + 54 = -2 Reorder the terms: 54 + 3n + 4n2 = -2 Solving 54 + 3n + 4n2 = -2 Solving for variable 'n'. Reorder the terms: 54 + 2 + 3n + 4n2 = -2 + 2 Combine like terms: 54 + 2 = 56 56 + 3n + 4n2 = -2 + 2 Combine like terms: -2 + 2 = 0 56 + 3n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14 + 0.75n + n2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 0.75n + -14 + n2 = 0 + -14 Reorder the terms: 14 + -14 + 0.75n + n2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 0.75n + n2 = 0 + -14 0.75n + n2 = 0 + -14 Combine like terms: 0 + -14 = -14 0.75n + n2 = -14 The n term is 0.75n. 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. 0.75n + 0.140625 + n2 = -14 + 0.140625 Reorder the terms: 0.140625 + 0.75n + n2 = -14 + 0.140625 Combine like terms: -14 + 0.140625 = -13.859375 0.140625 + 0.75n + n2 = -13.859375 Factor a perfect square on the left side: (n + 0.375)(n + 0.375) = -13.859375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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