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Simplifying 3 + -1(4 + 3x)(2x + 1) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) Reorder the terms: 3 + -1(4 + 3x)(1 + 2x) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) Multiply (4 + 3x) * (1 + 2x) 3 + -1(4(1 + 2x) + 3x * (1 + 2x)) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + -1((1 * 4 + 2x * 4) + 3x * (1 + 2x)) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + -1((4 + 8x) + 3x * (1 + 2x)) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + -1(4 + 8x + (1 * 3x + 2x * 3x)) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + -1(4 + 8x + (3x + 6x2)) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) Combine like terms: 8x + 3x = 11x 3 + -1(4 + 11x + 6x2) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + (4 * -1 + 11x * -1 + 6x2 * -1) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) 3 + (-4 + -11x + -6x2) = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) Combine like terms: 3 + -4 = -1 -1 + -11x + -6x2 = 6x + -1(3x + -2)(x + 1) + -1(6 + -3x)(x + -1) Reorder the terms: -1 + -11x + -6x2 = 6x + -1(-2 + 3x)(x + 1) + -1(6 + -3x)(x + -1) Reorder the terms: -1 + -11x + -6x2 = 6x + -1(-2 + 3x)(1 + x) + -1(6 + -3x)(x + -1) Multiply (-2 + 3x) * (1 + x) -1 + -11x + -6x2 = 6x + -1(-2(1 + x) + 3x * (1 + x)) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + -1((1 * -2 + x * -2) + 3x * (1 + x)) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + -1((-2 + -2x) + 3x * (1 + x)) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + -1(-2 + -2x + (1 * 3x + x * 3x)) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + -1(-2 + -2x + (3x + 3x2)) + -1(6 + -3x)(x + -1) Combine like terms: -2x + 3x = 1x -1 + -11x + -6x2 = 6x + -1(-2 + 1x + 3x2) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + (-2 * -1 + 1x * -1 + 3x2 * -1) + -1(6 + -3x)(x + -1) -1 + -11x + -6x2 = 6x + (2 + -1x + -3x2) + -1(6 + -3x)(x + -1) Reorder the terms: -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1(6 + -3x)(-1 + x) Multiply (6 + -3x) * (-1 + x) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1(6(-1 + x) + -3x * (-1 + x)) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1((-1 * 6 + x * 6) + -3x * (-1 + x)) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1((-6 + 6x) + -3x * (-1 + x)) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1(-6 + 6x + (-1 * -3x + x * -3x)) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1(-6 + 6x + (3x + -3x2)) Combine like terms: 6x + 3x = 9x -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + -1(-6 + 9x + -3x2) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + (-6 * -1 + 9x * -1 + -3x2 * -1) -1 + -11x + -6x2 = 6x + 2 + -1x + -3x2 + (6 + -9x + 3x2) Reorder the terms: -1 + -11x + -6x2 = 2 + 6 + 6x + -1x + -9x + -3x2 + 3x2 Combine like terms: 2 + 6 = 8 -1 + -11x + -6x2 = 8 + 6x + -1x + -9x + -3x2 + 3x2 Combine like terms: 6x + -1x = 5x -1 + -11x + -6x2 = 8 + 5x + -9x + -3x2 + 3x2 Combine like terms: 5x + -9x = -4x -1 + -11x + -6x2 = 8 + -4x + -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -1 + -11x + -6x2 = 8 + -4x + 0 -1 + -11x + -6x2 = 8 + -4x Solving -1 + -11x + -6x2 = 8 + -4x Solving for variable 'x'. Reorder the terms: -1 + -8 + -11x + 4x + -6x2 = 8 + -4x + -8 + 4x Combine like terms: -1 + -8 = -9 -9 + -11x + 4x + -6x2 = 8 + -4x + -8 + 4x Combine like terms: -11x + 4x = -7x -9 + -7x + -6x2 = 8 + -4x + -8 + 4x Reorder the terms: -9 + -7x + -6x2 = 8 + -8 + -4x + 4x Combine like terms: 8 + -8 = 0 -9 + -7x + -6x2 = 0 + -4x + 4x -9 + -7x + -6x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -9 + -7x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 7x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying 9 + 7x + 6x2 = 0 Solving 9 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.166666667x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.166666667x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.166666667x + x2 = 0 + -1.5 1.166666667x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.166666667x + x2 = -1.5 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = -1.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = -1.5 + 0.3402777780 Combine like terms: -1.5 + 0.3402777780 = -1.159722222 0.3402777780 + 1.166666667x + x2 = -1.159722222 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = -1.159722222 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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