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Simplifying 2(x + -11) = 6x(x + 3) Reorder the terms: 2(-11 + x) = 6x(x + 3) (-11 * 2 + x * 2) = 6x(x + 3) (-22 + 2x) = 6x(x + 3) Reorder the terms: -22 + 2x = 6x(3 + x) -22 + 2x = (3 * 6x + x * 6x) -22 + 2x = (18x + 6x2) Solving -22 + 2x = 18x + 6x2 Solving for variable 'x'. Combine like terms: 2x + -18x = -16x -22 + -16x + -6x2 = 18x + 6x2 + -18x + -6x2 Reorder the terms: -22 + -16x + -6x2 = 18x + -18x + 6x2 + -6x2 Combine like terms: 18x + -18x = 0 -22 + -16x + -6x2 = 0 + 6x2 + -6x2 -22 + -16x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -22 + -16x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(11 + 8x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(11 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 11 + 8x + 3x2 = 0 Solving 11 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + 2.666666667x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + 2.666666667x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + -3.666666667 2.666666667x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 2.666666667x + x2 = -3.666666667 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 = -3.666666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -3.666666667 + 1.777777780 Combine like terms: -3.666666667 + 1.777777780 = -1.888888887 1.777777780 + 2.666666667x + x2 = -1.888888887 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -1.888888887 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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