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Simplifying (3x + -1) + -1(2x + 5) + -3(2x + -1)(x + 2) = 24 Reorder the terms: (-1 + 3x) + -1(2x + 5) + -3(2x + -1)(x + 2) = 24 Remove parenthesis around (-1 + 3x) -1 + 3x + -1(2x + 5) + -3(2x + -1)(x + 2) = 24 Reorder the terms: -1 + 3x + -1(5 + 2x) + -3(2x + -1)(x + 2) = 24 -1 + 3x + (5 * -1 + 2x * -1) + -3(2x + -1)(x + 2) = 24 -1 + 3x + (-5 + -2x) + -3(2x + -1)(x + 2) = 24 Reorder the terms: -1 + 3x + -5 + -2x + -3(-1 + 2x)(x + 2) = 24 Reorder the terms: -1 + 3x + -5 + -2x + -3(-1 + 2x)(2 + x) = 24 Multiply (-1 + 2x) * (2 + x) -1 + 3x + -5 + -2x + -3(-1(2 + x) + 2x * (2 + x)) = 24 -1 + 3x + -5 + -2x + -3((2 * -1 + x * -1) + 2x * (2 + x)) = 24 -1 + 3x + -5 + -2x + -3((-2 + -1x) + 2x * (2 + x)) = 24 -1 + 3x + -5 + -2x + -3(-2 + -1x + (2 * 2x + x * 2x)) = 24 -1 + 3x + -5 + -2x + -3(-2 + -1x + (4x + 2x2)) = 24 Combine like terms: -1x + 4x = 3x -1 + 3x + -5 + -2x + -3(-2 + 3x + 2x2) = 24 -1 + 3x + -5 + -2x + (-2 * -3 + 3x * -3 + 2x2 * -3) = 24 -1 + 3x + -5 + -2x + (6 + -9x + -6x2) = 24 Reorder the terms: -1 + -5 + 6 + 3x + -2x + -9x + -6x2 = 24 Combine like terms: -1 + -5 = -6 -6 + 6 + 3x + -2x + -9x + -6x2 = 24 Combine like terms: -6 + 6 = 0 0 + 3x + -2x + -9x + -6x2 = 24 3x + -2x + -9x + -6x2 = 24 Combine like terms: 3x + -2x = 1x 1x + -9x + -6x2 = 24 Combine like terms: 1x + -9x = -8x -8x + -6x2 = 24 Solving -8x + -6x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -8x + -6x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -8x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(12 + 4x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(12 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + 4x + 3x2 = 0 Solving 12 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 1.333333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 1.333333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 1.333333333x + x2 = 0 + -4 1.333333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 1.333333333x + x2 = -4 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -4 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -4 + 0.4444444442 Combine like terms: -4 + 0.4444444442 = -3.5555555558 0.4444444442 + 1.333333333x + x2 = -3.5555555558 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -3.5555555558 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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