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Simplifying (x + -1(-5 + 3i))(x + 5 + 3i)((x2) + 4) = 0 (x + (-5 * -1 + 3i * -1))(x + 5 + 3i)((x2) + 4) = 0 (x + (5 + -3i))(x + 5 + 3i)((x2) + 4) = 0 Reorder the terms: (5 + -3i + x)(x + 5 + 3i)((x2) + 4) = 0 Reorder the terms: (5 + -3i + x)(5 + 3i + x)((x2) + 4) = 0 (5 + -3i + x)(5 + 3i + x)(x2 + 4) = 0 Reorder the terms: (5 + -3i + x)(5 + 3i + x)(4 + x2) = 0 Multiply (5 + -3i + x) * (5 + 3i + x) (5(5 + 3i + x) + -3i * (5 + 3i + x) + x(5 + 3i + x))(4 + x2) = 0 ((5 * 5 + 3i * 5 + x * 5) + -3i * (5 + 3i + x) + x(5 + 3i + x))(4 + x2) = 0 ((25 + 15i + 5x) + -3i * (5 + 3i + x) + x(5 + 3i + x))(4 + x2) = 0 (25 + 15i + 5x + (5 * -3i + 3i * -3i + x * -3i) + x(5 + 3i + x))(4 + x2) = 0 Reorder the terms: (25 + 15i + 5x + (-15i + -3ix + -9i2) + x(5 + 3i + x))(4 + x2) = 0 (25 + 15i + 5x + (-15i + -3ix + -9i2) + x(5 + 3i + x))(4 + x2) = 0 (25 + 15i + 5x + -15i + -3ix + -9i2 + (5 * x + 3i * x + x * x))(4 + x2) = 0 Reorder the terms: (25 + 15i + 5x + -15i + -3ix + -9i2 + (3ix + 5x + x2))(4 + x2) = 0 (25 + 15i + 5x + -15i + -3ix + -9i2 + (3ix + 5x + x2))(4 + x2) = 0 Reorder the terms: (25 + 15i + -15i + -3ix + 3ix + -9i2 + 5x + 5x + x2)(4 + x2) = 0 Combine like terms: 15i + -15i = 0 (25 + 0 + -3ix + 3ix + -9i2 + 5x + 5x + x2)(4 + x2) = 0 (25 + -3ix + 3ix + -9i2 + 5x + 5x + x2)(4 + x2) = 0 Combine like terms: -3ix + 3ix = 0 (25 + 0 + -9i2 + 5x + 5x + x2)(4 + x2) = 0 (25 + -9i2 + 5x + 5x + x2)(4 + x2) = 0 Combine like terms: 5x + 5x = 10x (25 + -9i2 + 10x + x2)(4 + x2) = 0 Multiply (25 + -9i2 + 10x + x2) * (4 + x2) (25(4 + x2) + -9i2 * (4 + x2) + 10x * (4 + x2) + x2(4 + x2)) = 0 ((4 * 25 + x2 * 25) + -9i2 * (4 + x2) + 10x * (4 + x2) + x2(4 + x2)) = 0 ((100 + 25x2) + -9i2 * (4 + x2) + 10x * (4 + x2) + x2(4 + x2)) = 0 (100 + 25x2 + (4 * -9i2 + x2 * -9i2) + 10x * (4 + x2) + x2(4 + x2)) = 0 (100 + 25x2 + (-36i2 + -9i2x2) + 10x * (4 + x2) + x2(4 + x2)) = 0 (100 + 25x2 + -36i2 + -9i2x2 + (4 * 10x + x2 * 10x) + x2(4 + x2)) = 0 (100 + 25x2 + -36i2 + -9i2x2 + (40x + 10x3) + x2(4 + x2)) = 0 (100 + 25x2 + -36i2 + -9i2x2 + 40x + 10x3 + (4 * x2 + x2 * x2)) = 0 (100 + 25x2 + -36i2 + -9i2x2 + 40x + 10x3 + (4x2 + x4)) = 0 Reorder the terms: (100 + -36i2 + -9i2x2 + 40x + 25x2 + 4x2 + 10x3 + x4) = 0 Combine like terms: 25x2 + 4x2 = 29x2 (100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4) = 0 Solving 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + 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 + -9i2x2 + 40x + 29x2 + 10x3 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -100 -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -100 Add '-40x' to each side of the equation. -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + -40x + x4 = -100 + -40x Reorder the terms: -36i2 + -9i2x2 + 40x + -40x + 29x2 + 10x3 + x4 = -100 + -40x Combine like terms: 40x + -40x = 0 -36i2 + -9i2x2 + 0 + 29x2 + 10x3 + x4 = -100 + -40x -36i2 + -9i2x2 + 29x2 + 10x3 + x4 = -100 + -40x Add '-29x2' to each side of the equation. -36i2 + -9i2x2 + 29x2 + 10x3 + -29x2 + x4 = -100 + -40x + -29x2 Reorder the terms: -36i2 + -9i2x2 + 29x2 + -29x2 + 10x3 + x4 = -100 + -40x + -29x2 Combine like terms: 29x2 + -29x2 = 0 -36i2 + -9i2x2 + 0 + 10x3 + x4 = -100 + -40x + -29x2 -36i2 + -9i2x2 + 10x3 + x4 = -100 + -40x + -29x2 Add '-10x3' to each side of the equation. -36i2 + -9i2x2 + 10x3 + -10x3 + x4 = -100 + -40x + -29x2 + -10x3 Combine like terms: 10x3 + -10x3 = 0 -36i2 + -9i2x2 + 0 + x4 = -100 + -40x + -29x2 + -10x3 -36i2 + -9i2x2 + x4 = -100 + -40x + -29x2 + -10x3 Add '-1x4' to each side of the equation. -36i2 + -9i2x2 + x4 + -1x4 = -100 + -40x + -29x2 + -10x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -36i2 + -9i2x2 + 0 = -100 + -40x + -29x2 + -10x3 + -1x4 -36i2 + -9i2x2 = -100 + -40x + -29x2 + -10x3 + -1x4 Reorder the terms: 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -100 + -40x + -29x2 + -10x3 + -1x4 + 100 + 40x + 29x2 + 10x3 + x4 Reorder the terms: 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -100 + 100 + -40x + 40x + -29x2 + 29x2 + -10x3 + 10x3 + -1x4 + x4 Combine like terms: -100 + 100 = 0 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -40x + 40x + -29x2 + 29x2 + -10x3 + 10x3 + -1x4 + x4 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -40x + 40x + -29x2 + 29x2 + -10x3 + 10x3 + -1x4 + x4 Combine like terms: -40x + 40x = 0 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -29x2 + 29x2 + -10x3 + 10x3 + -1x4 + x4 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -29x2 + 29x2 + -10x3 + 10x3 + -1x4 + x4 Combine like terms: -29x2 + 29x2 = 0 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -10x3 + 10x3 + -1x4 + x4 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -10x3 + 10x3 + -1x4 + x4 Combine like terms: -10x3 + 10x3 = 0 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 + -1x4 + x4 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 100 + -36i2 + -9i2x2 + 40x + 29x2 + 10x3 + x4 = 0 The solution to this equation could not be determined.
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