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Simplifying 3n2 = 108n + -1028 Reorder the terms: 3n2 = -1028 + 108n Solving 3n2 = -1028 + 108n Solving for variable 'n'. Reorder the terms: 1028 + -108n + 3n2 = -1028 + 108n + 1028 + -108n Reorder the terms: 1028 + -108n + 3n2 = -1028 + 1028 + 108n + -108n Combine like terms: -1028 + 1028 = 0 1028 + -108n + 3n2 = 0 + 108n + -108n 1028 + -108n + 3n2 = 108n + -108n Combine like terms: 108n + -108n = 0 1028 + -108n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 342.6666667 + -36n + n2 = 0 Move the constant term to the right: Add '-342.6666667' to each side of the equation. 342.6666667 + -36n + -342.6666667 + n2 = 0 + -342.6666667 Reorder the terms: 342.6666667 + -342.6666667 + -36n + n2 = 0 + -342.6666667 Combine like terms: 342.6666667 + -342.6666667 = 0.0000000 0.0000000 + -36n + n2 = 0 + -342.6666667 -36n + n2 = 0 + -342.6666667 Combine like terms: 0 + -342.6666667 = -342.6666667 -36n + n2 = -342.6666667 The n term is -36n. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36n + 324 + n2 = -342.6666667 + 324 Reorder the terms: 324 + -36n + n2 = -342.6666667 + 324 Combine like terms: -342.6666667 + 324 = -18.6666667 324 + -36n + n2 = -18.6666667 Factor a perfect square on the left side: (n + -18)(n + -18) = -18.6666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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