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Simplifying n(n + 1) + 3 = 0 Reorder the terms: n(1 + n) + 3 = 0 (1 * n + n * n) + 3 = 0 (1n + n2) + 3 = 0 Reorder the terms: 3 + 1n + n2 = 0 Solving 3 + 1n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1n + -3 + n2 = 0 + -3 Reorder the terms: 3 + -3 + 1n + n2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1n + n2 = 0 + -3 1n + n2 = 0 + -3 Combine like terms: 0 + -3 = -3 1n + n2 = -3 The n term is 1n. 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. n + 0.25 + n2 = -3 + 0.25 Reorder the terms: 0.25 + n + n2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + n + n2 = -2.75 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -2.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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