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Simplifying (3x + 1)(3x + 1) + -1(3x + -2)(2x + 3x) = 17 Reorder the terms: (1 + 3x)(3x + 1) + -1(3x + -2)(2x + 3x) = 17 Reorder the terms: (1 + 3x)(1 + 3x) + -1(3x + -2)(2x + 3x) = 17 Multiply (1 + 3x) * (1 + 3x) (1(1 + 3x) + 3x * (1 + 3x)) + -1(3x + -2)(2x + 3x) = 17 ((1 * 1 + 3x * 1) + 3x * (1 + 3x)) + -1(3x + -2)(2x + 3x) = 17 ((1 + 3x) + 3x * (1 + 3x)) + -1(3x + -2)(2x + 3x) = 17 (1 + 3x + (1 * 3x + 3x * 3x)) + -1(3x + -2)(2x + 3x) = 17 (1 + 3x + (3x + 9x2)) + -1(3x + -2)(2x + 3x) = 17 Combine like terms: 3x + 3x = 6x (1 + 6x + 9x2) + -1(3x + -2)(2x + 3x) = 17 Reorder the terms: 1 + 6x + 9x2 + -1(-2 + 3x)(2x + 3x) = 17 Combine like terms: 2x + 3x = 5x 1 + 6x + 9x2 + -1(-2 + 3x)(5x) = 17 Remove parenthesis around (5x) 1 + 6x + 9x2 + -1(-2 + 3x) * 5x = 17 Reorder the terms for easier multiplication: 1 + 6x + 9x2 + -1 * 5x(-2 + 3x) = 17 Multiply -1 * 5 1 + 6x + 9x2 + -5x(-2 + 3x) = 17 1 + 6x + 9x2 + (-2 * -5x + 3x * -5x) = 17 1 + 6x + 9x2 + (10x + -15x2) = 17 Reorder the terms: 1 + 6x + 10x + 9x2 + -15x2 = 17 Combine like terms: 6x + 10x = 16x 1 + 16x + 9x2 + -15x2 = 17 Combine like terms: 9x2 + -15x2 = -6x2 1 + 16x + -6x2 = 17 Solving 1 + 16x + -6x2 = 17 Solving for variable 'x'. Reorder the terms: 1 + -17 + 16x + -6x2 = 17 + -17 Combine like terms: 1 + -17 = -16 -16 + 16x + -6x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -16 + 16x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 8x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 8x + -3x2)' equal to zero and attempt to solve: Simplifying -8 + 8x + -3x2 = 0 Solving -8 + 8x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 2.666666667 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -2.666666667x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + -2.666666667 -2.666666667x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -2.666666667x + x2 = -2.666666667 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 = -2.666666667 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -2.666666667 + 1.777777780 Combine like terms: -2.666666667 + 1.777777780 = -0.888888887 1.777777780 + -2.666666667x + x2 = -0.888888887 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -0.888888887 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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