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Simplifying 2x + 3x(4x + -5) = 3x + -6 Reorder the terms: 2x + 3x(-5 + 4x) = 3x + -6 2x + (-5 * 3x + 4x * 3x) = 3x + -6 2x + (-15x + 12x2) = 3x + -6 Combine like terms: 2x + -15x = -13x -13x + 12x2 = 3x + -6 Reorder the terms: -13x + 12x2 = -6 + 3x Solving -13x + 12x2 = -6 + 3x Solving for variable 'x'. Reorder the terms: 6 + -13x + -3x + 12x2 = -6 + 3x + 6 + -3x Combine like terms: -13x + -3x = -16x 6 + -16x + 12x2 = -6 + 3x + 6 + -3x Reorder the terms: 6 + -16x + 12x2 = -6 + 6 + 3x + -3x Combine like terms: -6 + 6 = 0 6 + -16x + 12x2 = 0 + 3x + -3x 6 + -16x + 12x2 = 3x + -3x Combine like terms: 3x + -3x = 0 6 + -16x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -8x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -8x + 6x2)' equal to zero and attempt to solve: Simplifying 3 + -8x + 6x2 = 0 Solving 3 + -8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.333333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.333333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.333333333x + x2 = 0 + -0.5 -1.333333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.333333333x + x2 = -0.5 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 = -0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.5 + 0.4444444442 Combine like terms: -0.5 + 0.4444444442 = -0.0555555558 0.4444444442 + -1.333333333x + x2 = -0.0555555558 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -0.0555555558 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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