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Simplifying 5 + 8 + 4n2 + 4n + 1 + 6n2 + n = 0 Reorder the terms: 5 + 8 + 1 + 4n + n + 4n2 + 6n2 = 0 Combine like terms: 5 + 8 = 13 13 + 1 + 4n + n + 4n2 + 6n2 = 0 Combine like terms: 13 + 1 = 14 14 + 4n + n + 4n2 + 6n2 = 0 Combine like terms: 4n + n = 5n 14 + 5n + 4n2 + 6n2 = 0 Combine like terms: 4n2 + 6n2 = 10n2 14 + 5n + 10n2 = 0 Solving 14 + 5n + 10n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.4 + 0.5n + n2 = 0.0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 0.5n + -1.4 + n2 = 0.0 + -1.4 Reorder the terms: 1.4 + -1.4 + 0.5n + n2 = 0.0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 0.5n + n2 = 0.0 + -1.4 0.5n + n2 = 0.0 + -1.4 Combine like terms: 0.0 + -1.4 = -1.4 0.5n + n2 = -1.4 The n term is 0.5n. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5n + 0.0625 + n2 = -1.4 + 0.0625 Reorder the terms: 0.0625 + 0.5n + n2 = -1.4 + 0.0625 Combine like terms: -1.4 + 0.0625 = -1.3375 0.0625 + 0.5n + n2 = -1.3375 Factor a perfect square on the left side: (n + 0.25)(n + 0.25) = -1.3375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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