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Simplifying 6x(3x + -1) + -2x = 2(2x + -5) + -8 Reorder the terms: 6x(-1 + 3x) + -2x = 2(2x + -5) + -8 (-1 * 6x + 3x * 6x) + -2x = 2(2x + -5) + -8 (-6x + 18x2) + -2x = 2(2x + -5) + -8 Reorder the terms: -6x + -2x + 18x2 = 2(2x + -5) + -8 Combine like terms: -6x + -2x = -8x -8x + 18x2 = 2(2x + -5) + -8 Reorder the terms: -8x + 18x2 = 2(-5 + 2x) + -8 -8x + 18x2 = (-5 * 2 + 2x * 2) + -8 -8x + 18x2 = (-10 + 4x) + -8 Reorder the terms: -8x + 18x2 = -10 + -8 + 4x Combine like terms: -10 + -8 = -18 -8x + 18x2 = -18 + 4x Solving -8x + 18x2 = -18 + 4x Solving for variable 'x'. Reorder the terms: 18 + -8x + -4x + 18x2 = -18 + 4x + 18 + -4x Combine like terms: -8x + -4x = -12x 18 + -12x + 18x2 = -18 + 4x + 18 + -4x Reorder the terms: 18 + -12x + 18x2 = -18 + 18 + 4x + -4x Combine like terms: -18 + 18 = 0 18 + -12x + 18x2 = 0 + 4x + -4x 18 + -12x + 18x2 = 4x + -4x Combine like terms: 4x + -4x = 0 18 + -12x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + -2x + 3x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + -2x + 3x2 = 0 Solving 3 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.6666666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.6666666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.6666666667x + x2 = 0 + -1 -0.6666666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.6666666667x + x2 = -1 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 = -1 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1 + 0.1111111112 Combine like terms: -1 + 0.1111111112 = -0.8888888888 0.1111111112 + -0.6666666667x + x2 = -0.8888888888 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.8888888888 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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