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Simplifying 12x4 + -6x2 + 6 = 0 Reorder the terms: 6 + -6x2 + 12x4 = 0 Solving 6 + -6x2 + 12x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -1x2 + 2x4) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -1x2 + 2x4)' equal to zero and attempt to solve: Simplifying 1 + -1x2 + 2x4 = 0 Solving 1 + -1x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.5x2 + -0.5 + x4 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.5x2 + x4 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.5x2 + x4 = 0 + -0.5 -0.5x2 + x4 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.5x2 + x4 = -0.5 The x term is -0.5x2. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x2 + 0.0625 + x4 = -0.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = -0.5 + 0.0625 Combine like terms: -0.5 + 0.0625 = -0.4375 0.0625 + -0.5x2 + x4 = -0.4375 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = -0.4375 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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