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Simplifying (x + -5)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-5 + x)(x + -2 + i)(x + -2 + -1i) = 0 Reorder the terms: (-5 + x)(-2 + i + x)(x + -2 + -1i) = 0 Reorder the terms: (-5 + x)(-2 + i + x)(-2 + -1i + x) = 0 Multiply (-5 + x) * (-2 + i + x) (-5(-2 + i + x) + x(-2 + i + x))(-2 + -1i + x) = 0 ((-2 * -5 + i * -5 + x * -5) + x(-2 + i + x))(-2 + -1i + x) = 0 ((10 + -5i + -5x) + x(-2 + i + x))(-2 + -1i + x) = 0 (10 + -5i + -5x + (-2 * x + i * x + x * x))(-2 + -1i + x) = 0 Reorder the terms: (10 + -5i + -5x + (ix + -2x + x2))(-2 + -1i + x) = 0 (10 + -5i + -5x + (ix + -2x + x2))(-2 + -1i + x) = 0 Reorder the terms: (10 + -5i + ix + -5x + -2x + x2)(-2 + -1i + x) = 0 Combine like terms: -5x + -2x = -7x (10 + -5i + ix + -7x + x2)(-2 + -1i + x) = 0 Multiply (10 + -5i + ix + -7x + x2) * (-2 + -1i + x) (10(-2 + -1i + x) + -5i * (-2 + -1i + x) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-2 * 10 + -1i * 10 + x * 10) + -5i * (-2 + -1i + x) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 ((-20 + -10i + 10x) + -5i * (-2 + -1i + x) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + (-2 * -5i + -1i * -5i + x * -5i) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-20 + -10i + 10x + (10i + -5ix + 5i2) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + (10i + -5ix + 5i2) + ix(-2 + -1i + x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + (-2 * ix + -1i * ix + x * ix) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-20 + -10i + 10x + 10i + -5ix + 5i2 + (-2ix + ix2 + -1i2x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + (-2ix + ix2 + -1i2x) + -7x * (-2 + -1i + x) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + (-2 * -7x + -1i * -7x + x * -7x) + x2(-2 + -1i + x)) = 0 Reorder the terms: (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + (7ix + 14x + -7x2) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + (7ix + 14x + -7x2) + x2(-2 + -1i + x)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + 7ix + 14x + -7x2 + (-2 * x2 + -1i * x2 + x * x2)) = 0 Reorder the terms: (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + 7ix + 14x + -7x2 + (-1ix2 + -2x2 + x3)) = 0 (-20 + -10i + 10x + 10i + -5ix + 5i2 + -2ix + ix2 + -1i2x + 7ix + 14x + -7x2 + (-1ix2 + -2x2 + x3)) = 0 Reorder the terms: (-20 + -10i + 10i + -5ix + -2ix + 7ix + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 Combine like terms: -10i + 10i = 0 (-20 + 0 + -5ix + -2ix + 7ix + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 (-20 + -5ix + -2ix + 7ix + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 Combine like terms: -5ix + -2ix = -7ix (-20 + -7ix + 7ix + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 Combine like terms: -7ix + 7ix = 0 (-20 + 0 + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 (-20 + ix2 + -1ix2 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 Combine like terms: ix2 + -1ix2 = 0 (-20 + 0 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 (-20 + 5i2 + -1i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0 Combine like terms: 10x + 14x = 24x (-20 + 5i2 + -1i2x + 24x + -7x2 + -2x2 + x3) = 0 Combine like terms: -7x2 + -2x2 = -9x2 (-20 + 5i2 + -1i2x + 24x + -9x2 + x3) = 0 Solving -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 5i2 + -1i2x + 24x + -9x2 + 20 + x3 = 0 + 20 Reorder the terms: -20 + 20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + 20 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + 20 Combine like terms: 0 + 20 = 20 5i2 + -1i2x + 24x + -9x2 + x3 = 20 Add '-24x' to each side of the equation. 5i2 + -1i2x + 24x + -9x2 + -24x + x3 = 20 + -24x Reorder the terms: 5i2 + -1i2x + 24x + -24x + -9x2 + x3 = 20 + -24x Combine like terms: 24x + -24x = 0 5i2 + -1i2x + 0 + -9x2 + x3 = 20 + -24x 5i2 + -1i2x + -9x2 + x3 = 20 + -24x Add '9x2' to each side of the equation. 5i2 + -1i2x + -9x2 + 9x2 + x3 = 20 + -24x + 9x2 Combine like terms: -9x2 + 9x2 = 0 5i2 + -1i2x + 0 + x3 = 20 + -24x + 9x2 5i2 + -1i2x + x3 = 20 + -24x + 9x2 Add '-1x3' to each side of the equation. 5i2 + -1i2x + x3 + -1x3 = 20 + -24x + 9x2 + -1x3 Combine like terms: x3 + -1x3 = 0 5i2 + -1i2x + 0 = 20 + -24x + 9x2 + -1x3 5i2 + -1i2x = 20 + -24x + 9x2 + -1x3 Reorder the terms: -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 20 + -24x + 9x2 + -1x3 + -20 + 24x + -9x2 + x3 Reorder the terms: -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 20 + -20 + -24x + 24x + 9x2 + -9x2 + -1x3 + x3 Combine like terms: 20 + -20 = 0 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + -24x + 24x + 9x2 + -9x2 + -1x3 + x3 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = -24x + 24x + 9x2 + -9x2 + -1x3 + x3 Combine like terms: -24x + 24x = 0 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + 9x2 + -9x2 + -1x3 + x3 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 9x2 + -9x2 + -1x3 + x3 Combine like terms: 9x2 + -9x2 = 0 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 + -1x3 + x3 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -20 + 5i2 + -1i2x + 24x + -9x2 + x3 = 0 The solution to this equation could not be determined.
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