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Simplifying 4x4 + -12x2 + 32 = 0 Reorder the terms: 32 + -12x2 + 4x4 = 0 Solving 32 + -12x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -3x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -3x2 + x4)' equal to zero and attempt to solve: Simplifying 8 + -3x2 + x4 = 0 Solving 8 + -3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -3x2 + -8 + x4 = 0 + -8 Reorder the terms: 8 + -8 + -3x2 + x4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x2 + x4 = 0 + -8 -3x2 + x4 = 0 + -8 Combine like terms: 0 + -8 = -8 -3x2 + x4 = -8 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -8 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -8 + 2.25 Combine like terms: -8 + 2.25 = -5.75 2.25 + -3x2 + x4 = -5.75 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = -5.75 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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