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Simplifying 3n2 = 105n + -1028 Reorder the terms: 3n2 = -1028 + 105n Solving 3n2 = -1028 + 105n Solving for variable 'n'. Reorder the terms: 1028 + -105n + 3n2 = -1028 + 105n + 1028 + -105n Reorder the terms: 1028 + -105n + 3n2 = -1028 + 1028 + 105n + -105n Combine like terms: -1028 + 1028 = 0 1028 + -105n + 3n2 = 0 + 105n + -105n 1028 + -105n + 3n2 = 105n + -105n Combine like terms: 105n + -105n = 0 1028 + -105n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 342.6666667 + -35n + n2 = 0 Move the constant term to the right: Add '-342.6666667' to each side of the equation. 342.6666667 + -35n + -342.6666667 + n2 = 0 + -342.6666667 Reorder the terms: 342.6666667 + -342.6666667 + -35n + n2 = 0 + -342.6666667 Combine like terms: 342.6666667 + -342.6666667 = 0.0000000 0.0000000 + -35n + n2 = 0 + -342.6666667 -35n + n2 = 0 + -342.6666667 Combine like terms: 0 + -342.6666667 = -342.6666667 -35n + n2 = -342.6666667 The n term is -35n. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35n + 306.25 + n2 = -342.6666667 + 306.25 Reorder the terms: 306.25 + -35n + n2 = -342.6666667 + 306.25 Combine like terms: -342.6666667 + 306.25 = -36.4166667 306.25 + -35n + n2 = -36.4166667 Factor a perfect square on the left side: (n + -17.5)(n + -17.5) = -36.4166667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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