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Simplifying 12 + 4(3x + -2)(4x + -3) = 0 Reorder the terms: 12 + 4(-2 + 3x)(4x + -3) = 0 Reorder the terms: 12 + 4(-2 + 3x)(-3 + 4x) = 0 Multiply (-2 + 3x) * (-3 + 4x) 12 + 4(-2(-3 + 4x) + 3x * (-3 + 4x)) = 0 12 + 4((-3 * -2 + 4x * -2) + 3x * (-3 + 4x)) = 0 12 + 4((6 + -8x) + 3x * (-3 + 4x)) = 0 12 + 4(6 + -8x + (-3 * 3x + 4x * 3x)) = 0 12 + 4(6 + -8x + (-9x + 12x2)) = 0 Combine like terms: -8x + -9x = -17x 12 + 4(6 + -17x + 12x2) = 0 12 + (6 * 4 + -17x * 4 + 12x2 * 4) = 0 12 + (24 + -68x + 48x2) = 0 Combine like terms: 12 + 24 = 36 36 + -68x + 48x2 = 0 Solving 36 + -68x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -17x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -17x + 12x2)' equal to zero and attempt to solve: Simplifying 9 + -17x + 12x2 = 0 Solving 9 + -17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -1.416666667x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -1.416666667x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -1.416666667x + x2 = 0 + -0.75 -1.416666667x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -1.416666667x + x2 = -0.75 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = -0.75 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = -0.75 + 0.5017361113 Combine like terms: -0.75 + 0.5017361113 = -0.2482638887 0.5017361113 + -1.416666667x + x2 = -0.2482638887 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = -0.2482638887 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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