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Simplifying -2x(4 + 3x) = 6 + -4x (4 * -2x + 3x * -2x) = 6 + -4x (-8x + -6x2) = 6 + -4x Solving -8x + -6x2 = 6 + -4x Solving for variable 'x'. Reorder the terms: -6 + -8x + 4x + -6x2 = 6 + -4x + -6 + 4x Combine like terms: -8x + 4x = -4x -6 + -4x + -6x2 = 6 + -4x + -6 + 4x Reorder the terms: -6 + -4x + -6x2 = 6 + -6 + -4x + 4x Combine like terms: 6 + -6 = 0 -6 + -4x + -6x2 = 0 + -4x + 4x -6 + -4x + -6x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -6 + -4x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 2x + 3x2) = 0 Ignore the factor -2.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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