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Simplifying (x + 2)(x + -9 + -4i)(x + -9 + 4i) = 0 Reorder the terms: (2 + x)(x + -9 + -4i)(x + -9 + 4i) = 0 Reorder the terms: (2 + x)(-9 + -4i + x)(x + -9 + 4i) = 0 Reorder the terms: (2 + x)(-9 + -4i + x)(-9 + 4i + x) = 0 Multiply (2 + x) * (-9 + -4i + x) (2(-9 + -4i + x) + x(-9 + -4i + x))(-9 + 4i + x) = 0 ((-9 * 2 + -4i * 2 + x * 2) + x(-9 + -4i + x))(-9 + 4i + x) = 0 ((-18 + -8i + 2x) + x(-9 + -4i + x))(-9 + 4i + x) = 0 (-18 + -8i + 2x + (-9 * x + -4i * x + x * x))(-9 + 4i + x) = 0 Reorder the terms: (-18 + -8i + 2x + (-4ix + -9x + x2))(-9 + 4i + x) = 0 (-18 + -8i + 2x + (-4ix + -9x + x2))(-9 + 4i + x) = 0 Reorder the terms: (-18 + -8i + -4ix + 2x + -9x + x2)(-9 + 4i + x) = 0 Combine like terms: 2x + -9x = -7x (-18 + -8i + -4ix + -7x + x2)(-9 + 4i + x) = 0 Multiply (-18 + -8i + -4ix + -7x + x2) * (-9 + 4i + x) (-18(-9 + 4i + x) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 ((-9 * -18 + 4i * -18 + x * -18) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 ((162 + -72i + -18x) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + (-9 * -8i + 4i * -8i + x * -8i) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 Reorder the terms: (162 + -72i + -18x + (72i + -8ix + -32i2) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + (72i + -8ix + -32i2) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + (-9 * -4ix + 4i * -4ix + x * -4ix) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 Reorder the terms: (162 + -72i + -18x + 72i + -8ix + -32i2 + (36ix + -4ix2 + -16i2x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + (36ix + -4ix2 + -16i2x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-9 * -7x + 4i * -7x + x * -7x) + x2(-9 + 4i + x)) = 0 Reorder the terms: (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-28ix + 63x + -7x2) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-28ix + 63x + -7x2) + x2(-9 + 4i + x)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (-9 * x2 + 4i * x2 + x * x2)) = 0 Reorder the terms: (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (4ix2 + -9x2 + x3)) = 0 (162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (4ix2 + -9x2 + x3)) = 0 Reorder the terms: (162 + -72i + 72i + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 Combine like terms: -72i + 72i = 0 (162 + 0 + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 (162 + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 Combine like terms: -8ix + 36ix = 28ix (162 + 28ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 Combine like terms: 28ix + -28ix = 0 (162 + 0 + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 (162 + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 Combine like terms: -4ix2 + 4ix2 = 0 (162 + 0 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 (162 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0 Combine like terms: -18x + 63x = 45x (162 + -32i2 + -16i2x + 45x + -7x2 + -9x2 + x3) = 0 Combine like terms: -7x2 + -9x2 = -16x2 (162 + -32i2 + -16i2x + 45x + -16x2 + x3) = 0 Solving 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-162' to each side of the equation. 162 + -32i2 + -16i2x + 45x + -16x2 + -162 + x3 = 0 + -162 Reorder the terms: 162 + -162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162 Combine like terms: 162 + -162 = 0 0 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162 -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162 Combine like terms: 0 + -162 = -162 -32i2 + -16i2x + 45x + -16x2 + x3 = -162 Add '-45x' to each side of the equation. -32i2 + -16i2x + 45x + -16x2 + -45x + x3 = -162 + -45x Reorder the terms: -32i2 + -16i2x + 45x + -45x + -16x2 + x3 = -162 + -45x Combine like terms: 45x + -45x = 0 -32i2 + -16i2x + 0 + -16x2 + x3 = -162 + -45x -32i2 + -16i2x + -16x2 + x3 = -162 + -45x Add '16x2' to each side of the equation. -32i2 + -16i2x + -16x2 + 16x2 + x3 = -162 + -45x + 16x2 Combine like terms: -16x2 + 16x2 = 0 -32i2 + -16i2x + 0 + x3 = -162 + -45x + 16x2 -32i2 + -16i2x + x3 = -162 + -45x + 16x2 Add '-1x3' to each side of the equation. -32i2 + -16i2x + x3 + -1x3 = -162 + -45x + 16x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -32i2 + -16i2x + 0 = -162 + -45x + 16x2 + -1x3 -32i2 + -16i2x = -162 + -45x + 16x2 + -1x3 Reorder the terms: 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -162 + -45x + 16x2 + -1x3 + 162 + 45x + -16x2 + x3 Reorder the terms: 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -162 + 162 + -45x + 45x + 16x2 + -16x2 + -1x3 + x3 Combine like terms: -162 + 162 = 0 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -45x + 45x + 16x2 + -16x2 + -1x3 + x3 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -45x + 45x + 16x2 + -16x2 + -1x3 + x3 Combine like terms: -45x + 45x = 0 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + 16x2 + -16x2 + -1x3 + x3 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 16x2 + -16x2 + -1x3 + x3 Combine like terms: 16x2 + -16x2 = 0 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -1x3 + x3 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 The solution to this equation could not be determined.
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