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Simplifying -1(3x + -1)(2x + 3) = 7 Reorder the terms: -1(-1 + 3x)(2x + 3) = 7 Reorder the terms: -1(-1 + 3x)(3 + 2x) = 7 Multiply (-1 + 3x) * (3 + 2x) -1(-1(3 + 2x) + 3x * (3 + 2x)) = 7 -1((3 * -1 + 2x * -1) + 3x * (3 + 2x)) = 7 -1((-3 + -2x) + 3x * (3 + 2x)) = 7 -1(-3 + -2x + (3 * 3x + 2x * 3x)) = 7 -1(-3 + -2x + (9x + 6x2)) = 7 Combine like terms: -2x + 9x = 7x -1(-3 + 7x + 6x2) = 7 (-3 * -1 + 7x * -1 + 6x2 * -1) = 7 (3 + -7x + -6x2) = 7 Solving 3 + -7x + -6x2 = 7 Solving for variable 'x'. Reorder the terms: 3 + -7 + -7x + -6x2 = 7 + -7 Combine like terms: 3 + -7 = -4 -4 + -7x + -6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -4 + -7x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 7x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 7x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + 6x2 = 0 Solving 4 + 7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 1.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 1.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + -0.6666666667 1.166666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 1.166666667x + x2 = -0.6666666667 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 = -0.6666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = -0.6666666667 + 0.3402777780 Combine like terms: -0.6666666667 + 0.3402777780 = -0.3263888887 0.3402777780 + 1.166666667x + x2 = -0.3263888887 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = -0.3263888887 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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