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Simplifying 2n2 + 3n + 9 = 0 Reorder the terms: 9 + 3n + 2n2 = 0 Solving 9 + 3n + 2n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 1.5n + n2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 1.5n + -4.5 + n2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 1.5n + n2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 1.5n + n2 = 0 + -4.5 1.5n + n2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 1.5n + n2 = -4.5 The n term is 1.5n. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5n + 0.5625 + n2 = -4.5 + 0.5625 Reorder the terms: 0.5625 + 1.5n + n2 = -4.5 + 0.5625 Combine like terms: -4.5 + 0.5625 = -3.9375 0.5625 + 1.5n + n2 = -3.9375 Factor a perfect square on the left side: (n + 0.75)(n + 0.75) = -3.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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