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Simplifying 2(x + -3 + 2x) + -1x(2 + 6 + 3x) = 0 Reorder the terms: 2(-3 + x + 2x) + -1x(2 + 6 + 3x) = 0 Combine like terms: x + 2x = 3x 2(-3 + 3x) + -1x(2 + 6 + 3x) = 0 (-3 * 2 + 3x * 2) + -1x(2 + 6 + 3x) = 0 (-6 + 6x) + -1x(2 + 6 + 3x) = 0 Combine like terms: 2 + 6 = 8 -6 + 6x + -1x(8 + 3x) = 0 -6 + 6x + (8 * -1x + 3x * -1x) = 0 -6 + 6x + (-8x + -3x2) = 0 Combine like terms: 6x + -8x = -2x -6 + -2x + -3x2 = 0 Solving -6 + -2x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 2x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + 2x + 3x2 = 0 Solving 6 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.6666666667x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 0.6666666667x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.6666666667x + x2 = 0 + -2 0.6666666667x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.6666666667x + x2 = -2 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 = -2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -2 + 0.1111111112 Combine like terms: -2 + 0.1111111112 = -1.8888888888 0.1111111112 + 0.6666666667x + x2 = -1.8888888888 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -1.8888888888 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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