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Simplifying 9x2 = 6x + -6 Reorder the terms: 9x2 = -6 + 6x Solving 9x2 = -6 + 6x Solving for variable 'x'. Reorder the terms: 6 + -6x + 9x2 = -6 + 6x + 6 + -6x Reorder the terms: 6 + -6x + 9x2 = -6 + 6 + 6x + -6x Combine like terms: -6 + 6 = 0 6 + -6x + 9x2 = 0 + 6x + -6x 6 + -6x + 9x2 = 6x + -6x Combine like terms: 6x + -6x = 0 6 + -6x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -2x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + -2x + 3x2 = 0 Solving 2 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.6666666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.6666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + -0.6666666667 -0.6666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.6666666667x + x2 = -0.6666666667 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -0.6666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -0.6666666667 + 0.1111111112 Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555 0.1111111112 + -0.6666666667x + x2 = -0.5555555555 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.5555555555 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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