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Simplifying 4x(3x + -2) + -1(x + -3) = 0 Reorder the terms: 4x(-2 + 3x) + -1(x + -3) = 0 (-2 * 4x + 3x * 4x) + -1(x + -3) = 0 (-8x + 12x2) + -1(x + -3) = 0 Reorder the terms: -8x + 12x2 + -1(-3 + x) = 0 -8x + 12x2 + (-3 * -1 + x * -1) = 0 -8x + 12x2 + (3 + -1x) = 0 Reorder the terms: 3 + -8x + -1x + 12x2 = 0 Combine like terms: -8x + -1x = -9x 3 + -9x + 12x2 = 0 Solving 3 + -9x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -3x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -3x + 4x2 = 0 Solving 1 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.75x + x2 = 0 + -0.25 -0.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.75x + x2 = -0.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + -0.75x + x2 = -0.109375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.109375 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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