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Simplifying 10 + 3n + n2 + 8n + 9n2 + 2n = 0 Reorder the terms: 10 + 3n + 8n + 2n + n2 + 9n2 = 0 Combine like terms: 3n + 8n = 11n 10 + 11n + 2n + n2 + 9n2 = 0 Combine like terms: 11n + 2n = 13n 10 + 13n + n2 + 9n2 = 0 Combine like terms: n2 + 9n2 = 10n2 10 + 13n + 10n2 = 0 Solving 10 + 13n + 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 + 1.3n + n2 = 0.0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.3n + -1 + n2 = 0.0 + -1 Reorder the terms: 1 + -1 + 1.3n + n2 = 0.0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.3n + n2 = 0.0 + -1 1.3n + n2 = 0.0 + -1 Combine like terms: 0.0 + -1 = -1 1.3n + n2 = -1 The n term is 1.3n. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3n + 0.4225 + n2 = -1 + 0.4225 Reorder the terms: 0.4225 + 1.3n + n2 = -1 + 0.4225 Combine like terms: -1 + 0.4225 = -0.5775 0.4225 + 1.3n + n2 = -0.5775 Factor a perfect square on the left side: (n + 0.65)(n + 0.65) = -0.5775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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