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