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Simplifying 2x4 + 8x2 + 64 = 0 Reorder the terms: 64 + 8x2 + 2x4 = 0 Solving 64 + 8x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 4x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying 32 + 4x2 + x4 = 0 Solving 32 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 4x2 + -32 + x4 = 0 + -32 Reorder the terms: 32 + -32 + 4x2 + x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 4x2 + x4 = 0 + -32 4x2 + x4 = 0 + -32 Combine like terms: 0 + -32 = -32 4x2 + x4 = -32 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = -32 + 4 Reorder the terms: 4 + 4x2 + x4 = -32 + 4 Combine like terms: -32 + 4 = -28 4 + 4x2 + x4 = -28 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = -28 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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