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Simplifying (9n2 + 5n) + (n2 + 6n + 12) = 0 Reorder the terms: (5n + 9n2) + (n2 + 6n + 12) = 0 Remove parenthesis around (5n + 9n2) 5n + 9n2 + (n2 + 6n + 12) = 0 Reorder the terms: 5n + 9n2 + (12 + 6n + n2) = 0 Remove parenthesis around (12 + 6n + n2) 5n + 9n2 + 12 + 6n + n2 = 0 Reorder the terms: 12 + 5n + 6n + 9n2 + n2 = 0 Combine like terms: 5n + 6n = 11n 12 + 11n + 9n2 + n2 = 0 Combine like terms: 9n2 + n2 = 10n2 12 + 11n + 10n2 = 0 Solving 12 + 11n + 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'. 1.2 + 1.1n + n2 = 0.0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 1.1n + -1.2 + n2 = 0.0 + -1.2 Reorder the terms: 1.2 + -1.2 + 1.1n + n2 = 0.0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 1.1n + n2 = 0.0 + -1.2 1.1n + n2 = 0.0 + -1.2 Combine like terms: 0.0 + -1.2 = -1.2 1.1n + n2 = -1.2 The n term is 1.1n. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1n + 0.3025 + n2 = -1.2 + 0.3025 Reorder the terms: 0.3025 + 1.1n + n2 = -1.2 + 0.3025 Combine like terms: -1.2 + 0.3025 = -0.8975 0.3025 + 1.1n + n2 = -0.8975 Factor a perfect square on the left side: (n + 0.55)(n + 0.55) = -0.8975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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