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Simplifying 5n + 8 + 4n2 + 4n + 1 + 6n2 + n = 0 Reorder the terms: 8 + 1 + 5n + 4n + n + 4n2 + 6n2 = 0 Combine like terms: 8 + 1 = 9 9 + 5n + 4n + n + 4n2 + 6n2 = 0 Combine like terms: 5n + 4n = 9n 9 + 9n + n + 4n2 + 6n2 = 0 Combine like terms: 9n + n = 10n 9 + 10n + 4n2 + 6n2 = 0 Combine like terms: 4n2 + 6n2 = 10n2 9 + 10n + 10n2 = 0 Solving 9 + 10n + 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'. 0.9 + n + n2 = 0.0 Move the constant term to the right: Add '-0.9' to each side of the equation. 0.9 + n + -0.9 + n2 = 0.0 + -0.9 Reorder the terms: 0.9 + -0.9 + n + n2 = 0.0 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + n + n2 = 0.0 + -0.9 n + n2 = 0.0 + -0.9 Combine like terms: 0.0 + -0.9 = -0.9 n + n2 = -0.9 The n term is n. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + n2 = -0.9 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + n2 = -0.9 + 0.25 Combine like terms: -0.9 + 0.25 = -0.65 1.25 + n2 = -0.65 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -0.65 Can't calculate square root of the right side. The solution to this equation could not be determined.
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