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Simplifying 9n2 = -77 + 18n Solving 9n2 = -77 + 18n Solving for variable 'n'. Reorder the terms: 77 + -18n + 9n2 = -77 + 18n + 77 + -18n Reorder the terms: 77 + -18n + 9n2 = -77 + 77 + 18n + -18n Combine like terms: -77 + 77 = 0 77 + -18n + 9n2 = 0 + 18n + -18n 77 + -18n + 9n2 = 18n + -18n Combine like terms: 18n + -18n = 0 77 + -18n + 9n2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 8.555555556 + -2n + n2 = 0 Move the constant term to the right: Add '-8.555555556' to each side of the equation. 8.555555556 + -2n + -8.555555556 + n2 = 0 + -8.555555556 Reorder the terms: 8.555555556 + -8.555555556 + -2n + n2 = 0 + -8.555555556 Combine like terms: 8.555555556 + -8.555555556 = 0.000000000 0.000000000 + -2n + n2 = 0 + -8.555555556 -2n + n2 = 0 + -8.555555556 Combine like terms: 0 + -8.555555556 = -8.555555556 -2n + n2 = -8.555555556 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 = -8.555555556 + 1 Reorder the terms: 1 + -2n + n2 = -8.555555556 + 1 Combine like terms: -8.555555556 + 1 = -7.555555556 1 + -2n + n2 = -7.555555556 Factor a perfect square on the left side: (n + -1)(n + -1) = -7.555555556 Can't calculate square root of the right side. The solution to this equation could not be determined.
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