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Simplifying (x + -1)(x + -1)(x + 4i)(x + -4i) = 0 Reorder the terms: (-1 + x)(x + -1)(x + 4i)(x + -4i) = 0 Reorder the terms: (-1 + x)(-1 + x)(x + 4i)(x + -4i) = 0 Reorder the terms: (-1 + x)(-1 + x)(4i + x)(x + -4i) = 0 Reorder the terms: (-1 + x)(-1 + x)(4i + x)(-4i + x) = 0 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x))(4i + x)(-4i + x) = 0 ((-1 * -1 + x * -1) + x(-1 + x))(4i + x)(-4i + x) = 0 ((1 + -1x) + x(-1 + x))(4i + x)(-4i + x) = 0 (1 + -1x + (-1 * x + x * x))(4i + x)(-4i + x) = 0 (1 + -1x + (-1x + x2))(4i + x)(-4i + x) = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + x2)(4i + x)(-4i + x) = 0 Multiply (1 + -2x + x2) * (4i + x) (1(4i + x) + -2x * (4i + x) + x2(4i + x))(-4i + x) = 0 ((4i * 1 + x * 1) + -2x * (4i + x) + x2(4i + x))(-4i + x) = 0 ((4i + 1x) + -2x * (4i + x) + x2(4i + x))(-4i + x) = 0 (4i + 1x + (4i * -2x + x * -2x) + x2(4i + x))(-4i + x) = 0 (4i + 1x + (-8ix + -2x2) + x2(4i + x))(-4i + x) = 0 (4i + 1x + -8ix + -2x2 + (4i * x2 + x * x2))(-4i + x) = 0 (4i + 1x + -8ix + -2x2 + (4ix2 + x3))(-4i + x) = 0 Reorder the terms: (4i + -8ix + 4ix2 + 1x + -2x2 + x3)(-4i + x) = 0 (4i + -8ix + 4ix2 + 1x + -2x2 + x3)(-4i + x) = 0 Multiply (4i + -8ix + 4ix2 + 1x + -2x2 + x3) * (-4i + x) (4i * (-4i + x) + -8ix * (-4i + x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 ((-4i * 4i + x * 4i) + -8ix * (-4i + x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 Reorder the terms: ((4ix + -16i2) + -8ix * (-4i + x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 ((4ix + -16i2) + -8ix * (-4i + x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + (-4i * -8ix + x * -8ix) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 Reorder the terms: (4ix + -16i2 + (-8ix2 + 32i2x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + (-8ix2 + 32i2x) + 4ix2 * (-4i + x) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + (-4i * 4ix2 + x * 4ix2) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 Reorder the terms: (4ix + -16i2 + -8ix2 + 32i2x + (4ix3 + -16i2x2) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + (4ix3 + -16i2x2) + 1x * (-4i + x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + (-4i * 1x + x * 1x) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + (-4ix + 1x2) + -2x2 * (-4i + x) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + -4ix + 1x2 + (-4i * -2x2 + x * -2x2) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + -4ix + 1x2 + (8ix2 + -2x3) + x3(-4i + x)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + -4ix + 1x2 + 8ix2 + -2x3 + (-4i * x3 + x * x3)) = 0 (4ix + -16i2 + -8ix2 + 32i2x + 4ix3 + -16i2x2 + -4ix + 1x2 + 8ix2 + -2x3 + (-4ix3 + x4)) = 0 Reorder the terms: (4ix + -4ix + -8ix2 + 8ix2 + 4ix3 + -4ix3 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 Combine like terms: 4ix + -4ix = 0 (0 + -8ix2 + 8ix2 + 4ix3 + -4ix3 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 (-8ix2 + 8ix2 + 4ix3 + -4ix3 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 Combine like terms: -8ix2 + 8ix2 = 0 (0 + 4ix3 + -4ix3 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 (4ix3 + -4ix3 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 Combine like terms: 4ix3 + -4ix3 = 0 (0 + -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 (-16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4) = 0 Solving -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1x2' to each side of the equation. -16i2 + 32i2x + -16i2x2 + 1x2 + -2x3 + -1x2 + x4 = 0 + -1x2 Reorder the terms: -16i2 + 32i2x + -16i2x2 + 1x2 + -1x2 + -2x3 + x4 = 0 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -16i2 + 32i2x + -16i2x2 + 0 + -2x3 + x4 = 0 + -1x2 -16i2 + 32i2x + -16i2x2 + -2x3 + x4 = 0 + -1x2 Remove the zero: -16i2 + 32i2x + -16i2x2 + -2x3 + x4 = -1x2 Add '2x3' to each side of the equation. -16i2 + 32i2x + -16i2x2 + -2x3 + 2x3 + x4 = -1x2 + 2x3 Combine like terms: -2x3 + 2x3 = 0 -16i2 + 32i2x + -16i2x2 + 0 + x4 = -1x2 + 2x3 -16i2 + 32i2x + -16i2x2 + x4 = -1x2 + 2x3 Add '-1x4' to each side of the equation. -16i2 + 32i2x + -16i2x2 + x4 + -1x4 = -1x2 + 2x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -16i2 + 32i2x + -16i2x2 + 0 = -1x2 + 2x3 + -1x4 -16i2 + 32i2x + -16i2x2 = -1x2 + 2x3 + -1x4 Reorder the terms: -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = -1x2 + x2 + 2x3 + -2x3 + -1x4 + x4 Combine like terms: -1x2 + x2 = 0 -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = 0 + 2x3 + -2x3 + -1x4 + x4 -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = 2x3 + -2x3 + -1x4 + x4 Combine like terms: 2x3 + -2x3 = 0 -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = 0 + -1x4 + x4 -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -16i2 + 32i2x + -16i2x2 + x2 + -2x3 + x4 = 0 The solution to this equation could not be determined.
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