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Simplifying 8x4 + -12x2 + 16 = 0 Reorder the terms: 16 + -12x2 + 8x4 = 0 Solving 16 + -12x2 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -3x2 + 2x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -3x2 + 2x4)' equal to zero and attempt to solve: Simplifying 4 + -3x2 + 2x4 = 0 Solving 4 + -3x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -1.5x2 + x4 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.5x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -1.5x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.5x2 + x4 = 0 + -2 -1.5x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.5x2 + x4 = -2 The x term is -1.5x2. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x2 + 0.5625 + x4 = -2 + 0.5625 Reorder the terms: 0.5625 + -1.5x2 + x4 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + -1.5x2 + x4 = -1.4375 Factor a perfect square on the left side: (x2 + -0.75)(x2 + -0.75) = -1.4375 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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