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Simplifying 0 = 3x2 + -11x + 51 Reorder the terms: 0 = 51 + -11x + 3x2 Solving 0 = 51 + -11x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -51 = -51 -51 + 11x + -3x2 = 51 + -11x + 3x2 + -51 + 11x + -3x2 Reorder the terms: -51 + 11x + -3x2 = 51 + -51 + -11x + 11x + 3x2 + -3x2 Combine like terms: 51 + -51 = 0 -51 + 11x + -3x2 = 0 + -11x + 11x + 3x2 + -3x2 -51 + 11x + -3x2 = -11x + 11x + 3x2 + -3x2 Combine like terms: -11x + 11x = 0 -51 + 11x + -3x2 = 0 + 3x2 + -3x2 -51 + 11x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -51 + 11x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 17 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '-17' to each side of the equation. 17 + -3.666666667x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + -3.666666667x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -3.666666667x + x2 = 0 + -17 -3.666666667x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 -3.666666667x + x2 = -17 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = -17 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = -17 + 3.361111114 Combine like terms: -17 + 3.361111114 = -13.638888886 3.361111114 + -3.666666667x + x2 = -13.638888886 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = -13.638888886 Can't calculate square root of the right side. The solution to this equation could not be determined.
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