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Simplifying 12x2 + -9x + 24 = 0 Reorder the terms: 24 + -9x + 12x2 = 0 Solving 24 + -9x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + -3x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + -3x + 4x2 = 0 Solving 8 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -0.75x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.75x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.75x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.75x + x2 = 0 + -2 -0.75x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.75x + x2 = -2 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 = -2 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -2 + 0.140625 Combine like terms: -2 + 0.140625 = -1.859375 0.140625 + -0.75x + x2 = -1.859375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -1.859375 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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