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Simplifying n(4n + 7) = -17 Reorder the terms: n(7 + 4n) = -17 (7 * n + 4n * n) = -17 (7n + 4n2) = -17 Solving 7n + 4n2 = -17 Solving for variable 'n'. Reorder the terms: 17 + 7n + 4n2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 7n + 4n2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + 1.75n + n2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + 1.75n + -4.25 + n2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + 1.75n + n2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + 1.75n + n2 = 0 + -4.25 1.75n + n2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 1.75n + n2 = -4.25 The n term is 1.75n. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75n + 0.765625 + n2 = -4.25 + 0.765625 Reorder the terms: 0.765625 + 1.75n + n2 = -4.25 + 0.765625 Combine like terms: -4.25 + 0.765625 = -3.484375 0.765625 + 1.75n + n2 = -3.484375 Factor a perfect square on the left side: (n + 0.875)(n + 0.875) = -3.484375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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