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Simplifying x + -6 = 3x2 + 9x Reorder the terms: -6 + x = 3x2 + 9x Reorder the terms: -6 + x = 9x + 3x2 Solving -6 + x = 9x + 3x2 Solving for variable 'x'. Combine like terms: x + -9x = -8x -6 + -8x + -3x2 = 9x + 3x2 + -9x + -3x2 Reorder the terms: -6 + -8x + -3x2 = 9x + -9x + 3x2 + -3x2 Combine like terms: 9x + -9x = 0 -6 + -8x + -3x2 = 0 + 3x2 + -3x2 -6 + -8x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + -8x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 8x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + 8x + 3x2 = 0 Solving 6 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2.666666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2.666666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2.666666667x + x2 = 0 + -2 2.666666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2.666666667x + x2 = -2 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -2 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -2 + 1.777777780 Combine like terms: -2 + 1.777777780 = -0.22222222 1.777777780 + 2.666666667x + x2 = -0.22222222 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -0.22222222 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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