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Simplifying (x + -8)(x + -5 + i)(x + -5 + -1i) = 0 Reorder the terms: (-8 + x)(x + -5 + i)(x + -5 + -1i) = 0 Reorder the terms: (-8 + x)(-5 + i + x)(x + -5 + -1i) = 0 Reorder the terms: (-8 + x)(-5 + i + x)(-5 + -1i + x) = 0 Multiply (-8 + x) * (-5 + i + x) (-8(-5 + i + x) + x(-5 + i + x))(-5 + -1i + x) = 0 ((-5 * -8 + i * -8 + x * -8) + x(-5 + i + x))(-5 + -1i + x) = 0 ((40 + -8i + -8x) + x(-5 + i + x))(-5 + -1i + x) = 0 (40 + -8i + -8x + (-5 * x + i * x + x * x))(-5 + -1i + x) = 0 Reorder the terms: (40 + -8i + -8x + (ix + -5x + x2))(-5 + -1i + x) = 0 (40 + -8i + -8x + (ix + -5x + x2))(-5 + -1i + x) = 0 Reorder the terms: (40 + -8i + ix + -8x + -5x + x2)(-5 + -1i + x) = 0 Combine like terms: -8x + -5x = -13x (40 + -8i + ix + -13x + x2)(-5 + -1i + x) = 0 Multiply (40 + -8i + ix + -13x + x2) * (-5 + -1i + x) (40(-5 + -1i + x) + -8i * (-5 + -1i + x) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 ((-5 * 40 + -1i * 40 + x * 40) + -8i * (-5 + -1i + x) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 ((-200 + -40i + 40x) + -8i * (-5 + -1i + x) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + (-5 * -8i + -1i * -8i + x * -8i) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 Reorder the terms: (-200 + -40i + 40x + (40i + -8ix + 8i2) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + (40i + -8ix + 8i2) + ix(-5 + -1i + x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + (-5 * ix + -1i * ix + x * ix) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 Reorder the terms: (-200 + -40i + 40x + 40i + -8ix + 8i2 + (-5ix + ix2 + -1i2x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + (-5ix + ix2 + -1i2x) + -13x * (-5 + -1i + x) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + (-5 * -13x + -1i * -13x + x * -13x) + x2(-5 + -1i + x)) = 0 Reorder the terms: (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + (13ix + 65x + -13x2) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + (13ix + 65x + -13x2) + x2(-5 + -1i + x)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + 13ix + 65x + -13x2 + (-5 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + 13ix + 65x + -13x2 + (-1ix2 + -5x2 + x3)) = 0 (-200 + -40i + 40x + 40i + -8ix + 8i2 + -5ix + ix2 + -1i2x + 13ix + 65x + -13x2 + (-1ix2 + -5x2 + x3)) = 0 Reorder the terms: (-200 + -40i + 40i + -8ix + -5ix + 13ix + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 Combine like terms: -40i + 40i = 0 (-200 + 0 + -8ix + -5ix + 13ix + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 (-200 + -8ix + -5ix + 13ix + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 Combine like terms: -8ix + -5ix = -13ix (-200 + -13ix + 13ix + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 Combine like terms: -13ix + 13ix = 0 (-200 + 0 + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 (-200 + ix2 + -1ix2 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-200 + 0 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 (-200 + 8i2 + -1i2x + 40x + 65x + -13x2 + -5x2 + x3) = 0 Combine like terms: 40x + 65x = 105x (-200 + 8i2 + -1i2x + 105x + -13x2 + -5x2 + x3) = 0 Combine like terms: -13x2 + -5x2 = -18x2 (-200 + 8i2 + -1i2x + 105x + -18x2 + x3) = 0 Solving -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 8i2 + -1i2x + 105x + -18x2 + 200 + x3 = 0 + 200 Reorder the terms: -200 + 200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + 200 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + 200 Combine like terms: 0 + 200 = 200 8i2 + -1i2x + 105x + -18x2 + x3 = 200 Add '-105x' to each side of the equation. 8i2 + -1i2x + 105x + -18x2 + -105x + x3 = 200 + -105x Reorder the terms: 8i2 + -1i2x + 105x + -105x + -18x2 + x3 = 200 + -105x Combine like terms: 105x + -105x = 0 8i2 + -1i2x + 0 + -18x2 + x3 = 200 + -105x 8i2 + -1i2x + -18x2 + x3 = 200 + -105x Add '18x2' to each side of the equation. 8i2 + -1i2x + -18x2 + 18x2 + x3 = 200 + -105x + 18x2 Combine like terms: -18x2 + 18x2 = 0 8i2 + -1i2x + 0 + x3 = 200 + -105x + 18x2 8i2 + -1i2x + x3 = 200 + -105x + 18x2 Add '-1x3' to each side of the equation. 8i2 + -1i2x + x3 + -1x3 = 200 + -105x + 18x2 + -1x3 Combine like terms: x3 + -1x3 = 0 8i2 + -1i2x + 0 = 200 + -105x + 18x2 + -1x3 8i2 + -1i2x = 200 + -105x + 18x2 + -1x3 Reorder the terms: -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 200 + -105x + 18x2 + -1x3 + -200 + 105x + -18x2 + x3 Reorder the terms: -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 200 + -200 + -105x + 105x + 18x2 + -18x2 + -1x3 + x3 Combine like terms: 200 + -200 = 0 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + -105x + 105x + 18x2 + -18x2 + -1x3 + x3 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = -105x + 105x + 18x2 + -18x2 + -1x3 + x3 Combine like terms: -105x + 105x = 0 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + 18x2 + -18x2 + -1x3 + x3 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 18x2 + -18x2 + -1x3 + x3 Combine like terms: 18x2 + -18x2 = 0 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 + -1x3 + x3 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -200 + 8i2 + -1i2x + 105x + -18x2 + x3 = 0 The solution to this equation could not be determined.
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