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Simplifying 10n + 7 + 5n2 + 5n + 1 + 4n2 + n = 0 Reorder the terms: 7 + 1 + 10n + 5n + n + 5n2 + 4n2 = 0 Combine like terms: 7 + 1 = 8 8 + 10n + 5n + n + 5n2 + 4n2 = 0 Combine like terms: 10n + 5n = 15n 8 + 15n + n + 5n2 + 4n2 = 0 Combine like terms: 15n + n = 16n 8 + 16n + 5n2 + 4n2 = 0 Combine like terms: 5n2 + 4n2 = 9n2 8 + 16n + 9n2 = 0 Solving 8 + 16n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 1.777777778n + n2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 1.777777778n + -0.8888888889 + n2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 1.777777778n + n2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 1.777777778n + n2 = 0 + -0.8888888889 1.777777778n + n2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 1.777777778n + n2 = -0.8888888889 The n term is 1.777777778n. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778n + 0.7901234570 + n2 = -0.8888888889 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778n + n2 = -0.8888888889 + 0.7901234570 Combine like terms: -0.8888888889 + 0.7901234570 = -0.0987654319 0.7901234570 + 1.777777778n + n2 = -0.0987654319 Factor a perfect square on the left side: (n + 0.888888889)(n + 0.888888889) = -0.0987654319 Can't calculate square root of the right side. The solution to this equation could not be determined.
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