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Simplifying (x + 5 + -3i)(x + 5 + 3i)(x + -2)(x + -2) = 0 Reorder the terms: (5 + -3i + x)(x + 5 + 3i)(x + -2)(x + -2) = 0 Reorder the terms: (5 + -3i + x)(5 + 3i + x)(x + -2)(x + -2) = 0 Reorder the terms: (5 + -3i + x)(5 + 3i + x)(-2 + x)(x + -2) = 0 Reorder the terms: (5 + -3i + x)(5 + 3i + x)(-2 + x)(-2 + x) = 0 Multiply (5 + -3i + x) * (5 + 3i + x) (5(5 + 3i + x) + -3i * (5 + 3i + x) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 ((5 * 5 + 3i * 5 + x * 5) + -3i * (5 + 3i + x) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 ((25 + 15i + 5x) + -3i * (5 + 3i + x) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 (25 + 15i + 5x + (5 * -3i + 3i * -3i + x * -3i) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 Reorder the terms: (25 + 15i + 5x + (-15i + -3ix + -9i2) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 (25 + 15i + 5x + (-15i + -3ix + -9i2) + x(5 + 3i + x))(-2 + x)(-2 + x) = 0 (25 + 15i + 5x + -15i + -3ix + -9i2 + (5 * x + 3i * x + x * x))(-2 + x)(-2 + x) = 0 Reorder the terms: (25 + 15i + 5x + -15i + -3ix + -9i2 + (3ix + 5x + x2))(-2 + x)(-2 + x) = 0 (25 + 15i + 5x + -15i + -3ix + -9i2 + (3ix + 5x + x2))(-2 + x)(-2 + x) = 0 Reorder the terms: (25 + 15i + -15i + -3ix + 3ix + -9i2 + 5x + 5x + x2)(-2 + x)(-2 + x) = 0 Combine like terms: 15i + -15i = 0 (25 + 0 + -3ix + 3ix + -9i2 + 5x + 5x + x2)(-2 + x)(-2 + x) = 0 (25 + -3ix + 3ix + -9i2 + 5x + 5x + x2)(-2 + x)(-2 + x) = 0 Combine like terms: -3ix + 3ix = 0 (25 + 0 + -9i2 + 5x + 5x + x2)(-2 + x)(-2 + x) = 0 (25 + -9i2 + 5x + 5x + x2)(-2 + x)(-2 + x) = 0 Combine like terms: 5x + 5x = 10x (25 + -9i2 + 10x + x2)(-2 + x)(-2 + x) = 0 Multiply (25 + -9i2 + 10x + x2) * (-2 + x) (25(-2 + x) + -9i2 * (-2 + x) + 10x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 ((-2 * 25 + x * 25) + -9i2 * (-2 + x) + 10x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 ((-50 + 25x) + -9i2 * (-2 + x) + 10x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 (-50 + 25x + (-2 * -9i2 + x * -9i2) + 10x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 (-50 + 25x + (18i2 + -9i2x) + 10x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 (-50 + 25x + 18i2 + -9i2x + (-2 * 10x + x * 10x) + x2(-2 + x))(-2 + x) = 0 (-50 + 25x + 18i2 + -9i2x + (-20x + 10x2) + x2(-2 + x))(-2 + x) = 0 (-50 + 25x + 18i2 + -9i2x + -20x + 10x2 + (-2 * x2 + x * x2))(-2 + x) = 0 (-50 + 25x + 18i2 + -9i2x + -20x + 10x2 + (-2x2 + x3))(-2 + x) = 0 Reorder the terms: (-50 + 18i2 + -9i2x + 25x + -20x + 10x2 + -2x2 + x3)(-2 + x) = 0 Combine like terms: 25x + -20x = 5x (-50 + 18i2 + -9i2x + 5x + 10x2 + -2x2 + x3)(-2 + x) = 0 Combine like terms: 10x2 + -2x2 = 8x2 (-50 + 18i2 + -9i2x + 5x + 8x2 + x3)(-2 + x) = 0 Multiply (-50 + 18i2 + -9i2x + 5x + 8x2 + x3) * (-2 + x) (-50(-2 + x) + 18i2 * (-2 + x) + -9i2x * (-2 + x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 ((-2 * -50 + x * -50) + 18i2 * (-2 + x) + -9i2x * (-2 + x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 ((100 + -50x) + 18i2 * (-2 + x) + -9i2x * (-2 + x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + (-2 * 18i2 + x * 18i2) + -9i2x * (-2 + x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + (-36i2 + 18i2x) + -9i2x * (-2 + x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + (-2 * -9i2x + x * -9i2x) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + (18i2x + -9i2x2) + 5x * (-2 + x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + (-2 * 5x + x * 5x) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + (-10x + 5x2) + 8x2 * (-2 + x) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + -10x + 5x2 + (-2 * 8x2 + x * 8x2) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + -10x + 5x2 + (-16x2 + 8x3) + x3(-2 + x)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + -10x + 5x2 + -16x2 + 8x3 + (-2 * x3 + x * x3)) = 0 (100 + -50x + -36i2 + 18i2x + 18i2x + -9i2x2 + -10x + 5x2 + -16x2 + 8x3 + (-2x3 + x4)) = 0 Reorder the terms: (100 + -36i2 + 18i2x + 18i2x + -9i2x2 + -50x + -10x + 5x2 + -16x2 + 8x3 + -2x3 + x4) = 0 Combine like terms: 18i2x + 18i2x = 36i2x (100 + -36i2 + 36i2x + -9i2x2 + -50x + -10x + 5x2 + -16x2 + 8x3 + -2x3 + x4) = 0 Combine like terms: -50x + -10x = -60x (100 + -36i2 + 36i2x + -9i2x2 + -60x + 5x2 + -16x2 + 8x3 + -2x3 + x4) = 0 Combine like terms: 5x2 + -16x2 = -11x2 (100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 8x3 + -2x3 + x4) = 0 Combine like terms: 8x3 + -2x3 = 6x3 (100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4) = 0 Solving 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + -100 -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = -100 Add '60x' to each side of the equation. -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + 60x + x4 = -100 + 60x Reorder the terms: -36i2 + 36i2x + -9i2x2 + -60x + 60x + -11x2 + 6x3 + x4 = -100 + 60x Combine like terms: -60x + 60x = 0 -36i2 + 36i2x + -9i2x2 + 0 + -11x2 + 6x3 + x4 = -100 + 60x -36i2 + 36i2x + -9i2x2 + -11x2 + 6x3 + x4 = -100 + 60x Add '11x2' to each side of the equation. -36i2 + 36i2x + -9i2x2 + -11x2 + 6x3 + 11x2 + x4 = -100 + 60x + 11x2 Reorder the terms: -36i2 + 36i2x + -9i2x2 + -11x2 + 11x2 + 6x3 + x4 = -100 + 60x + 11x2 Combine like terms: -11x2 + 11x2 = 0 -36i2 + 36i2x + -9i2x2 + 0 + 6x3 + x4 = -100 + 60x + 11x2 -36i2 + 36i2x + -9i2x2 + 6x3 + x4 = -100 + 60x + 11x2 Add '-6x3' to each side of the equation. -36i2 + 36i2x + -9i2x2 + 6x3 + -6x3 + x4 = -100 + 60x + 11x2 + -6x3 Combine like terms: 6x3 + -6x3 = 0 -36i2 + 36i2x + -9i2x2 + 0 + x4 = -100 + 60x + 11x2 + -6x3 -36i2 + 36i2x + -9i2x2 + x4 = -100 + 60x + 11x2 + -6x3 Add '-1x4' to each side of the equation. -36i2 + 36i2x + -9i2x2 + x4 + -1x4 = -100 + 60x + 11x2 + -6x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -36i2 + 36i2x + -9i2x2 + 0 = -100 + 60x + 11x2 + -6x3 + -1x4 -36i2 + 36i2x + -9i2x2 = -100 + 60x + 11x2 + -6x3 + -1x4 Reorder the terms: 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = -100 + 60x + 11x2 + -6x3 + -1x4 + 100 + -60x + -11x2 + 6x3 + x4 Reorder the terms: 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = -100 + 100 + 60x + -60x + 11x2 + -11x2 + -6x3 + 6x3 + -1x4 + x4 Combine like terms: -100 + 100 = 0 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + 60x + -60x + 11x2 + -11x2 + -6x3 + 6x3 + -1x4 + x4 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 60x + -60x + 11x2 + -11x2 + -6x3 + 6x3 + -1x4 + x4 Combine like terms: 60x + -60x = 0 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + 11x2 + -11x2 + -6x3 + 6x3 + -1x4 + x4 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 11x2 + -11x2 + -6x3 + 6x3 + -1x4 + x4 Combine like terms: 11x2 + -11x2 = 0 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + -6x3 + 6x3 + -1x4 + x4 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = -6x3 + 6x3 + -1x4 + x4 Combine like terms: -6x3 + 6x3 = 0 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 + -1x4 + x4 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 100 + -36i2 + 36i2x + -9i2x2 + -60x + -11x2 + 6x3 + x4 = 0 The solution to this equation could not be determined.
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