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Simplifying x4 + 2x2 + 8 = 0 Reorder the terms: 8 + 2x2 + x4 = 0 Solving 8 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 2x2 + -8 + x4 = 0 + -8 Reorder the terms: 8 + -8 + 2x2 + x4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2x2 + x4 = 0 + -8 2x2 + x4 = 0 + -8 Combine like terms: 0 + -8 = -8 2x2 + x4 = -8 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -8 + 1 Reorder the terms: 1 + 2x2 + x4 = -8 + 1 Combine like terms: -8 + 1 = -7 1 + 2x2 + x4 = -7 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = -7 Can't calculate square root of the right side. The solution to this equation could not be determined.
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