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Simplifying 3n2 + -12n + 43 = 3 Reorder the terms: 43 + -12n + 3n2 = 3 Solving 43 + -12n + 3n2 = 3 Solving for variable 'n'. Reorder the terms: 43 + -3 + -12n + 3n2 = 3 + -3 Combine like terms: 43 + -3 = 40 40 + -12n + 3n2 = 3 + -3 Combine like terms: 3 + -3 = 0 40 + -12n + 3n2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 13.33333333 + -4n + n2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -4n + -13.33333333 + n2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -4n + n2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -4n + n2 = 0 + -13.33333333 -4n + n2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -4n + n2 = -13.33333333 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = -13.33333333 + 4 Reorder the terms: 4 + -4n + n2 = -13.33333333 + 4 Combine like terms: -13.33333333 + 4 = -9.33333333 4 + -4n + n2 = -9.33333333 Factor a perfect square on the left side: (n + -2)(n + -2) = -9.33333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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