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Simplifying 6n2 = -11 + 3n Solving 6n2 = -11 + 3n Solving for variable 'n'. Reorder the terms: 11 + -3n + 6n2 = -11 + 3n + 11 + -3n Reorder the terms: 11 + -3n + 6n2 = -11 + 11 + 3n + -3n Combine like terms: -11 + 11 = 0 11 + -3n + 6n2 = 0 + 3n + -3n 11 + -3n + 6n2 = 3n + -3n Combine like terms: 3n + -3n = 0 11 + -3n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + -0.5n + n2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + -0.5n + -1.833333333 + n2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + -0.5n + n2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + -0.5n + n2 = 0 + -1.833333333 -0.5n + n2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 -0.5n + n2 = -1.833333333 The n term is -0.5n. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5n + 0.0625 + n2 = -1.833333333 + 0.0625 Reorder the terms: 0.0625 + -0.5n + n2 = -1.833333333 + 0.0625 Combine like terms: -1.833333333 + 0.0625 = -1.770833333 0.0625 + -0.5n + n2 = -1.770833333 Factor a perfect square on the left side: (n + -0.25)(n + -0.25) = -1.770833333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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