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Simplifying 0 = 6x2 + -13x + 14 Reorder the terms: 0 = 14 + -13x + 6x2 Solving 0 = 14 + -13x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -14 = -14 -14 + 13x + -6x2 = 14 + -13x + 6x2 + -14 + 13x + -6x2 Reorder the terms: -14 + 13x + -6x2 = 14 + -14 + -13x + 13x + 6x2 + -6x2 Combine like terms: 14 + -14 = 0 -14 + 13x + -6x2 = 0 + -13x + 13x + 6x2 + -6x2 -14 + 13x + -6x2 = -13x + 13x + 6x2 + -6x2 Combine like terms: -13x + 13x = 0 -14 + 13x + -6x2 = 0 + 6x2 + -6x2 -14 + 13x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -14 + 13x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 2.333333333 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -2.166666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -2.166666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -2.166666667x + x2 = 0 + -2.333333333 -2.166666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -2.166666667x + x2 = -2.333333333 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = -2.333333333 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = -2.333333333 + 1.173611113 Combine like terms: -2.333333333 + 1.173611113 = -1.15972222 1.173611113 + -2.166666667x + x2 = -1.15972222 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = -1.15972222 Can't calculate square root of the right side. The solution to this equation could not be determined.
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