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Simplifying (x + 7 + -1i)(x + 7 + i)(x + -1) = 0 Reorder the terms: (7 + -1i + x)(x + 7 + i)(x + -1) = 0 Reorder the terms: (7 + -1i + x)(7 + i + x)(x + -1) = 0 Reorder the terms: (7 + -1i + x)(7 + i + x)(-1 + x) = 0 Multiply (7 + -1i + x) * (7 + i + x) (7(7 + i + x) + -1i * (7 + i + x) + x(7 + i + x))(-1 + x) = 0 ((7 * 7 + i * 7 + x * 7) + -1i * (7 + i + x) + x(7 + i + x))(-1 + x) = 0 ((49 + 7i + 7x) + -1i * (7 + i + x) + x(7 + i + x))(-1 + x) = 0 (49 + 7i + 7x + (7 * -1i + i * -1i + x * -1i) + x(7 + i + x))(-1 + x) = 0 Reorder the terms: (49 + 7i + 7x + (-7i + -1ix + -1i2) + x(7 + i + x))(-1 + x) = 0 (49 + 7i + 7x + (-7i + -1ix + -1i2) + x(7 + i + x))(-1 + x) = 0 (49 + 7i + 7x + -7i + -1ix + -1i2 + (7 * x + i * x + x * x))(-1 + x) = 0 Reorder the terms: (49 + 7i + 7x + -7i + -1ix + -1i2 + (ix + 7x + x2))(-1 + x) = 0 (49 + 7i + 7x + -7i + -1ix + -1i2 + (ix + 7x + x2))(-1 + x) = 0 Reorder the terms: (49 + 7i + -7i + -1ix + ix + -1i2 + 7x + 7x + x2)(-1 + x) = 0 Combine like terms: 7i + -7i = 0 (49 + 0 + -1ix + ix + -1i2 + 7x + 7x + x2)(-1 + x) = 0 (49 + -1ix + ix + -1i2 + 7x + 7x + x2)(-1 + x) = 0 Combine like terms: -1ix + ix = 0 (49 + 0 + -1i2 + 7x + 7x + x2)(-1 + x) = 0 (49 + -1i2 + 7x + 7x + x2)(-1 + x) = 0 Combine like terms: 7x + 7x = 14x (49 + -1i2 + 14x + x2)(-1 + x) = 0 Multiply (49 + -1i2 + 14x + x2) * (-1 + x) (49(-1 + x) + -1i2 * (-1 + x) + 14x * (-1 + x) + x2(-1 + x)) = 0 ((-1 * 49 + x * 49) + -1i2 * (-1 + x) + 14x * (-1 + x) + x2(-1 + x)) = 0 ((-49 + 49x) + -1i2 * (-1 + x) + 14x * (-1 + x) + x2(-1 + x)) = 0 (-49 + 49x + (-1 * -1i2 + x * -1i2) + 14x * (-1 + x) + x2(-1 + x)) = 0 (-49 + 49x + (1i2 + -1i2x) + 14x * (-1 + x) + x2(-1 + x)) = 0 (-49 + 49x + 1i2 + -1i2x + (-1 * 14x + x * 14x) + x2(-1 + x)) = 0 (-49 + 49x + 1i2 + -1i2x + (-14x + 14x2) + x2(-1 + x)) = 0 (-49 + 49x + 1i2 + -1i2x + -14x + 14x2 + (-1 * x2 + x * x2)) = 0 (-49 + 49x + 1i2 + -1i2x + -14x + 14x2 + (-1x2 + x3)) = 0 Reorder the terms: (-49 + 1i2 + -1i2x + 49x + -14x + 14x2 + -1x2 + x3) = 0 Combine like terms: 49x + -14x = 35x (-49 + 1i2 + -1i2x + 35x + 14x2 + -1x2 + x3) = 0 Combine like terms: 14x2 + -1x2 = 13x2 (-49 + 1i2 + -1i2x + 35x + 13x2 + x3) = 0 Solving -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 1i2 + -1i2x + 35x + 13x2 + 49 + x3 = 0 + 49 Reorder the terms: -49 + 49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + 49 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + 49 Combine like terms: 0 + 49 = 49 1i2 + -1i2x + 35x + 13x2 + x3 = 49 Add '-35x' to each side of the equation. 1i2 + -1i2x + 35x + 13x2 + -35x + x3 = 49 + -35x Reorder the terms: 1i2 + -1i2x + 35x + -35x + 13x2 + x3 = 49 + -35x Combine like terms: 35x + -35x = 0 1i2 + -1i2x + 0 + 13x2 + x3 = 49 + -35x 1i2 + -1i2x + 13x2 + x3 = 49 + -35x Add '-13x2' to each side of the equation. 1i2 + -1i2x + 13x2 + -13x2 + x3 = 49 + -35x + -13x2 Combine like terms: 13x2 + -13x2 = 0 1i2 + -1i2x + 0 + x3 = 49 + -35x + -13x2 1i2 + -1i2x + x3 = 49 + -35x + -13x2 Add '-1x3' to each side of the equation. 1i2 + -1i2x + x3 + -1x3 = 49 + -35x + -13x2 + -1x3 Combine like terms: x3 + -1x3 = 0 1i2 + -1i2x + 0 = 49 + -35x + -13x2 + -1x3 1i2 + -1i2x = 49 + -35x + -13x2 + -1x3 Reorder the terms: -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 49 + -35x + -13x2 + -1x3 + -49 + 35x + 13x2 + x3 Reorder the terms: -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 49 + -49 + -35x + 35x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: 49 + -49 = 0 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + -35x + 35x + -13x2 + 13x2 + -1x3 + x3 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = -35x + 35x + -13x2 + 13x2 + -1x3 + x3 Combine like terms: -35x + 35x = 0 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + -13x2 + 13x2 + -1x3 + x3 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = -13x2 + 13x2 + -1x3 + x3 Combine like terms: -13x2 + 13x2 = 0 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 + -1x3 + x3 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -49 + 1i2 + -1i2x + 35x + 13x2 + x3 = 0 The solution to this equation could not be determined.
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