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Simplifying 7n2 + n + 29 = 0 Reorder the terms: 29 + n + 7n2 = 0 Solving 29 + n + 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'. 4.142857143 + 0.1428571429n + n2 = 0 Move the constant term to the right: Add '-4.142857143' to each side of the equation. 4.142857143 + 0.1428571429n + -4.142857143 + n2 = 0 + -4.142857143 Reorder the terms: 4.142857143 + -4.142857143 + 0.1428571429n + n2 = 0 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + 0.1428571429n + n2 = 0 + -4.142857143 0.1428571429n + n2 = 0 + -4.142857143 Combine like terms: 0 + -4.142857143 = -4.142857143 0.1428571429n + n2 = -4.142857143 The n term is n. 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. 0.1428571429n + 0.25 + n2 = -4.142857143 + 0.25 Reorder the terms: 0.25 + 0.1428571429n + n2 = -4.142857143 + 0.25 Combine like terms: -4.142857143 + 0.25 = -3.892857143 0.25 + 0.1428571429n + n2 = -3.892857143 Factor a perfect square on the left side: (n + 0.5)(n + 0.5) = -3.892857143 Can't calculate square root of the right side. The solution to this equation could not be determined.
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