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Simplifying 8n2 + n = -11 Reorder the terms: n + 8n2 = -11 Solving n + 8n2 = -11 Solving for variable 'n'. Reorder the terms: 11 + n + 8n2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + n + 8n2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.375 + 0.125n + n2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + 0.125n + -1.375 + n2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + 0.125n + n2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + 0.125n + n2 = 0 + -1.375 0.125n + n2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 0.125n + n2 = -1.375 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. 0.125n + 0.25 + n2 = -1.375 + 0.25 Reorder the terms: 0.25 + 0.125n + n2 = -1.375 + 0.25 Combine like terms: -1.375 + 0.25 = -1.125 0.25 + 0.125n + n2 = -1.125 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -1.125 Can't calculate square root of the right side. The solution to this equation could not be determined.
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