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Simplifying n2 + 12n + 19 = -27 Reorder the terms: 19 + 12n + n2 = -27 Solving 19 + 12n + n2 = -27 Solving for variable 'n'. Reorder the terms: 19 + 27 + 12n + n2 = -27 + 27 Combine like terms: 19 + 27 = 46 46 + 12n + n2 = -27 + 27 Combine like terms: -27 + 27 = 0 46 + 12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + 12n + -46 + n2 = 0 + -46 Reorder the terms: 46 + -46 + 12n + n2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 12n + n2 = 0 + -46 12n + n2 = 0 + -46 Combine like terms: 0 + -46 = -46 12n + n2 = -46 The n term is 12n. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12n + 36 + n2 = -46 + 36 Reorder the terms: 36 + 12n + n2 = -46 + 36 Combine like terms: -46 + 36 = -10 36 + 12n + n2 = -10 Factor a perfect square on the left side: (n + 6)(n + 6) = -10 Can't calculate square root of the right side. The solution to this equation could not be determined.
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