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Simplifying 7n2 + -14n + 54 = -5 Reorder the terms: 54 + -14n + 7n2 = -5 Solving 54 + -14n + 7n2 = -5 Solving for variable 'n'. Reorder the terms: 54 + 5 + -14n + 7n2 = -5 + 5 Combine like terms: 54 + 5 = 59 59 + -14n + 7n2 = -5 + 5 Combine like terms: -5 + 5 = 0 59 + -14n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 8.428571429 + -2n + n2 = 0 Move the constant term to the right: Add '-8.428571429' to each side of the equation. 8.428571429 + -2n + -8.428571429 + n2 = 0 + -8.428571429 Reorder the terms: 8.428571429 + -8.428571429 + -2n + n2 = 0 + -8.428571429 Combine like terms: 8.428571429 + -8.428571429 = 0.000000000 0.000000000 + -2n + n2 = 0 + -8.428571429 -2n + n2 = 0 + -8.428571429 Combine like terms: 0 + -8.428571429 = -8.428571429 -2n + n2 = -8.428571429 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = -8.428571429 + 1 Reorder the terms: 1 + -2n + n2 = -8.428571429 + 1 Combine like terms: -8.428571429 + 1 = -7.428571429 1 + -2n + n2 = -7.428571429 Factor a perfect square on the left side: (n + -1)(n + -1) = -7.428571429 Can't calculate square root of the right side. The solution to this equation could not be determined.
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