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Simplifying 0 = 12x2 + -9x + 6 Reorder the terms: 0 = 6 + -9x + 12x2 Solving 0 = 6 + -9x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 9x + -12x2 = 6 + -9x + 12x2 + -6 + 9x + -12x2 Reorder the terms: -6 + 9x + -12x2 = 6 + -6 + -9x + 9x + 12x2 + -12x2 Combine like terms: 6 + -6 = 0 -6 + 9x + -12x2 = 0 + -9x + 9x + 12x2 + -12x2 -6 + 9x + -12x2 = -9x + 9x + 12x2 + -12x2 Combine like terms: -9x + 9x = 0 -6 + 9x + -12x2 = 0 + 12x2 + -12x2 -6 + 9x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -6 + 9x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying -2 + 3x + -4x2 = 0 Solving -2 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.75x + x2 = 0 + -0.5 -0.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.75x + x2 = -0.5 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 = -0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + -0.75x + x2 = -0.359375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.359375 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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