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Simplifying 4x4 + -20x2 + 64 = 0 Reorder the terms: 64 + -20x2 + 4x4 = 0 Solving 64 + -20x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(16 + -5x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(16 + -5x2 + x4)' equal to zero and attempt to solve: Simplifying 16 + -5x2 + x4 = 0 Solving 16 + -5x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -5x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -5x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -5x2 + x4 = 0 + -16 -5x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -5x2 + x4 = -16 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -16 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -16 + 6.25 Combine like terms: -16 + 6.25 = -9.75 6.25 + -5x2 + x4 = -9.75 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = -9.75 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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