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Simplifying x4 + -4x2 + 4 + 8x2 + 16 + -4 = 0 Reorder the terms: 4 + 16 + -4 + -4x2 + 8x2 + x4 = 0 Combine like terms: 4 + 16 = 20 20 + -4 + -4x2 + 8x2 + x4 = 0 Combine like terms: 20 + -4 = 16 16 + -4x2 + 8x2 + x4 = 0 Combine like terms: -4x2 + 8x2 = 4x2 16 + 4x2 + x4 = 0 Solving 16 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 4x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + 4x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4x2 + x4 = 0 + -16 4x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 4x2 + x4 = -16 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 = -16 + 4 Reorder the terms: 4 + 4x2 + x4 = -16 + 4 Combine like terms: -16 + 4 = -12 4 + 4x2 + x4 = -12 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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