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Simplifying x(6x + -6) = (6 + 8)(x + -7) Reorder the terms: x(-6 + 6x) = (6 + 8)(x + -7) (-6 * x + 6x * x) = (6 + 8)(x + -7) (-6x + 6x2) = (6 + 8)(x + -7) Combine like terms: 6 + 8 = 14 -6x + 6x2 = (14)(x + -7) Reorder the terms: -6x + 6x2 = 14(-7 + x) -6x + 6x2 = (-7 * 14 + x * 14) -6x + 6x2 = (-98 + 14x) Solving -6x + 6x2 = -98 + 14x Solving for variable 'x'. Reorder the terms: 98 + -6x + -14x + 6x2 = -98 + 14x + 98 + -14x Combine like terms: -6x + -14x = -20x 98 + -20x + 6x2 = -98 + 14x + 98 + -14x Reorder the terms: 98 + -20x + 6x2 = -98 + 98 + 14x + -14x Combine like terms: -98 + 98 = 0 98 + -20x + 6x2 = 0 + 14x + -14x 98 + -20x + 6x2 = 14x + -14x Combine like terms: 14x + -14x = 0 98 + -20x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -10x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + -10x + 3x2)' equal to zero and attempt to solve: Simplifying 49 + -10x + 3x2 = 0 Solving 49 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.33333333 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-16.33333333' to each side of the equation. 16.33333333 + -3.333333333x + -16.33333333 + x2 = 0 + -16.33333333 Reorder the terms: 16.33333333 + -16.33333333 + -3.333333333x + x2 = 0 + -16.33333333 Combine like terms: 16.33333333 + -16.33333333 = 0.00000000 0.00000000 + -3.333333333x + x2 = 0 + -16.33333333 -3.333333333x + x2 = 0 + -16.33333333 Combine like terms: 0 + -16.33333333 = -16.33333333 -3.333333333x + x2 = -16.33333333 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -16.33333333 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -16.33333333 + 2.777777779 Combine like terms: -16.33333333 + 2.777777779 = -13.555555551 2.777777779 + -3.333333333x + x2 = -13.555555551 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = -13.555555551 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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