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Simplifying 0 = 6x2 + -14x + 13 Reorder the terms: 0 = 13 + -14x + 6x2 Solving 0 = 13 + -14x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + 14x + -6x2 = 13 + -14x + 6x2 + -13 + 14x + -6x2 Reorder the terms: -13 + 14x + -6x2 = 13 + -13 + -14x + 14x + 6x2 + -6x2 Combine like terms: 13 + -13 = 0 -13 + 14x + -6x2 = 0 + -14x + 14x + 6x2 + -6x2 -13 + 14x + -6x2 = -14x + 14x + 6x2 + -6x2 Combine like terms: -14x + 14x = 0 -13 + 14x + -6x2 = 0 + 6x2 + -6x2 -13 + 14x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -13 + 14x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 2.166666667 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + -2.333333333x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + -2.333333333x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + -2.166666667 -2.333333333x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 -2.333333333x + x2 = -2.166666667 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -2.166666667 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -2.166666667 + 1.361111112 Combine like terms: -2.166666667 + 1.361111112 = -0.805555555 1.361111112 + -2.333333333x + x2 = -0.805555555 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = -0.805555555 Can't calculate square root of the right side. The solution to this equation could not be determined.
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