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Simplifying 7n2 + 23 + 6n = 0 Reorder the terms: 23 + 6n + 7n2 = 0 Solving 23 + 6n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.285714286 + 0.8571428571n + n2 = 0 Move the constant term to the right: Add '-3.285714286' to each side of the equation. 3.285714286 + 0.8571428571n + -3.285714286 + n2 = 0 + -3.285714286 Reorder the terms: 3.285714286 + -3.285714286 + 0.8571428571n + n2 = 0 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + 0.8571428571n + n2 = 0 + -3.285714286 0.8571428571n + n2 = 0 + -3.285714286 Combine like terms: 0 + -3.285714286 = -3.285714286 0.8571428571n + n2 = -3.285714286 The n term is 0.8571428571n. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571n + 0.1836734694 + n2 = -3.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571n + n2 = -3.285714286 + 0.1836734694 Combine like terms: -3.285714286 + 0.1836734694 = -3.1020408166 0.1836734694 + 0.8571428571n + n2 = -3.1020408166 Factor a perfect square on the left side: (n + 0.4285714286)(n + 0.4285714286) = -3.1020408166 Can't calculate square root of the right side. The solution to this equation could not be determined.
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