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Simplifying -6x2 = -9x + 13 Reorder the terms: -6x2 = 13 + -9x Solving -6x2 = 13 + -9x Solving for variable 'x'. Reorder the terms: -13 + 9x + -6x2 = 13 + -9x + -13 + 9x Reorder the terms: -13 + 9x + -6x2 = 13 + -13 + -9x + 9x Combine like terms: 13 + -13 = 0 -13 + 9x + -6x2 = 0 + -9x + 9x -13 + 9x + -6x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -13 + 9x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 2.166666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.166666667' to each side of the equation. 2.166666667 + -1.5x + -2.166666667 + x2 = 0 + -2.166666667 Reorder the terms: 2.166666667 + -2.166666667 + -1.5x + x2 = 0 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + -1.5x + x2 = 0 + -2.166666667 -1.5x + x2 = 0 + -2.166666667 Combine like terms: 0 + -2.166666667 = -2.166666667 -1.5x + x2 = -2.166666667 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -2.166666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.166666667 + 0.5625 Combine like terms: -2.166666667 + 0.5625 = -1.604166667 0.5625 + -1.5x + x2 = -1.604166667 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.604166667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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