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Simplifying (x + 5)(x + -5)(x + 2)(x + -2)(x + 2i)(x + -2i) = 0 Reorder the terms: (5 + x)(x + -5)(x + 2)(x + -2)(x + 2i)(x + -2i) = 0 Reorder the terms: (5 + x)(-5 + x)(x + 2)(x + -2)(x + 2i)(x + -2i) = 0 Reorder the terms: (5 + x)(-5 + x)(2 + x)(x + -2)(x + 2i)(x + -2i) = 0 Reorder the terms: (5 + x)(-5 + x)(2 + x)(-2 + x)(x + 2i)(x + -2i) = 0 Reorder the terms: (5 + x)(-5 + x)(2 + x)(-2 + x)(2i + x)(x + -2i) = 0 Reorder the terms: (5 + x)(-5 + x)(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 Multiply (5 + x) * (-5 + x) (5(-5 + x) + x(-5 + x))(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 ((-5 * 5 + x * 5) + x(-5 + x))(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 ((-25 + 5x) + x(-5 + x))(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 (-25 + 5x + (-5 * x + x * x))(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 (-25 + 5x + (-5x + x2))(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 Combine like terms: 5x + -5x = 0 (-25 + 0 + x2)(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 (-25 + x2)(2 + x)(-2 + x)(2i + x)(-2i + x) = 0 Multiply (-25 + x2) * (2 + x) (-25(2 + x) + x2(2 + x))(-2 + x)(2i + x)(-2i + x) = 0 ((2 * -25 + x * -25) + x2(2 + x))(-2 + x)(2i + x)(-2i + x) = 0 ((-50 + -25x) + x2(2 + x))(-2 + x)(2i + x)(-2i + x) = 0 (-50 + -25x + (2 * x2 + x * x2))(-2 + x)(2i + x)(-2i + x) = 0 (-50 + -25x + (2x2 + x3))(-2 + x)(2i + x)(-2i + x) = 0 (-50 + -25x + 2x2 + x3)(-2 + x)(2i + x)(-2i + x) = 0 Multiply (-50 + -25x + 2x2 + x3) * (-2 + x) (-50(-2 + x) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))(2i + x)(-2i + x) = 0 ((-2 * -50 + x * -50) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))(2i + x)(-2i + x) = 0 ((100 + -50x) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x))(2i + x)(-2i + x) = 0 (100 + -50x + (-2 * -25x + x * -25x) + 2x2 * (-2 + x) + x3(-2 + x))(2i + x)(-2i + x) = 0 (100 + -50x + (50x + -25x2) + 2x2 * (-2 + x) + x3(-2 + x))(2i + x)(-2i + x) = 0 (100 + -50x + 50x + -25x2 + (-2 * 2x2 + x * 2x2) + x3(-2 + x))(2i + x)(-2i + x) = 0 (100 + -50x + 50x + -25x2 + (-4x2 + 2x3) + x3(-2 + x))(2i + x)(-2i + x) = 0 (100 + -50x + 50x + -25x2 + -4x2 + 2x3 + (-2 * x3 + x * x3))(2i + x)(-2i + x) = 0 (100 + -50x + 50x + -25x2 + -4x2 + 2x3 + (-2x3 + x4))(2i + x)(-2i + x) = 0 Combine like terms: -50x + 50x = 0 (100 + 0 + -25x2 + -4x2 + 2x3 + -2x3 + x4)(2i + x)(-2i + x) = 0 (100 + -25x2 + -4x2 + 2x3 + -2x3 + x4)(2i + x)(-2i + x) = 0 Combine like terms: -25x2 + -4x2 = -29x2 (100 + -29x2 + 2x3 + -2x3 + x4)(2i + x)(-2i + x) = 0 Combine like terms: 2x3 + -2x3 = 0 (100 + -29x2 + 0 + x4)(2i + x)(-2i + x) = 0 (100 + -29x2 + x4)(2i + x)(-2i + x) = 0 Multiply (100 + -29x2 + x4) * (2i + x) (100(2i + x) + -29x2 * (2i + x) + x4(2i + x))(-2i + x) = 0 ((2i * 100 + x * 100) + -29x2 * (2i + x) + x4(2i + x))(-2i + x) = 0 ((200i + 100x) + -29x2 * (2i + x) + x4(2i + x))(-2i + x) = 0 (200i + 100x + (2i * -29x2 + x * -29x2) + x4(2i + x))(-2i + x) = 0 (200i + 100x + (-58ix2 + -29x3) + x4(2i + x))(-2i + x) = 0 (200i + 100x + -58ix2 + -29x3 + (2i * x4 + x * x4))(-2i + x) = 0 (200i + 100x + -58ix2 + -29x3 + (2ix4 + x5))(-2i + x) = 0 Reorder the terms: (200i + -58ix2 + 2ix4 + 100x + -29x3 + x5)(-2i + x) = 0 (200i + -58ix2 + 2ix4 + 100x + -29x3 + x5)(-2i + x) = 0 Multiply (200i + -58ix2 + 2ix4 + 100x + -29x3 + x5) * (-2i + x) (200i * (-2i + x) + -58ix2 * (-2i + x) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 ((-2i * 200i + x * 200i) + -58ix2 * (-2i + x) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 Reorder the terms: ((200ix + -400i2) + -58ix2 * (-2i + x) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 ((200ix + -400i2) + -58ix2 * (-2i + x) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + (-2i * -58ix2 + x * -58ix2) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 Reorder the terms: (200ix + -400i2 + (-58ix3 + 116i2x2) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + (-58ix3 + 116i2x2) + 2ix4 * (-2i + x) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + (-2i * 2ix4 + x * 2ix4) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 Reorder the terms: (200ix + -400i2 + -58ix3 + 116i2x2 + (2ix5 + -4i2x4) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + (2ix5 + -4i2x4) + 100x * (-2i + x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + (-2i * 100x + x * 100x) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + (-200ix + 100x2) + -29x3 * (-2i + x) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + -200ix + 100x2 + (-2i * -29x3 + x * -29x3) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + -200ix + 100x2 + (58ix3 + -29x4) + x5(-2i + x)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + -200ix + 100x2 + 58ix3 + -29x4 + (-2i * x5 + x * x5)) = 0 (200ix + -400i2 + -58ix3 + 116i2x2 + 2ix5 + -4i2x4 + -200ix + 100x2 + 58ix3 + -29x4 + (-2ix5 + x6)) = 0 Reorder the terms: (200ix + -200ix + -58ix3 + 58ix3 + 2ix5 + -2ix5 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 Combine like terms: 200ix + -200ix = 0 (0 + -58ix3 + 58ix3 + 2ix5 + -2ix5 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 (-58ix3 + 58ix3 + 2ix5 + -2ix5 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 Combine like terms: -58ix3 + 58ix3 = 0 (0 + 2ix5 + -2ix5 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 (2ix5 + -2ix5 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 Combine like terms: 2ix5 + -2ix5 = 0 (0 + -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 (-400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6) = 0 Solving -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-100x2' to each side of the equation. -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + -100x2 + x6 = 0 + -100x2 Reorder the terms: -400i2 + 116i2x2 + -4i2x4 + 100x2 + -100x2 + -29x4 + x6 = 0 + -100x2 Combine like terms: 100x2 + -100x2 = 0 -400i2 + 116i2x2 + -4i2x4 + 0 + -29x4 + x6 = 0 + -100x2 -400i2 + 116i2x2 + -4i2x4 + -29x4 + x6 = 0 + -100x2 Remove the zero: -400i2 + 116i2x2 + -4i2x4 + -29x4 + x6 = -100x2 Add '29x4' to each side of the equation. -400i2 + 116i2x2 + -4i2x4 + -29x4 + 29x4 + x6 = -100x2 + 29x4 Combine like terms: -29x4 + 29x4 = 0 -400i2 + 116i2x2 + -4i2x4 + 0 + x6 = -100x2 + 29x4 -400i2 + 116i2x2 + -4i2x4 + x6 = -100x2 + 29x4 Add '-1x6' to each side of the equation. -400i2 + 116i2x2 + -4i2x4 + x6 + -1x6 = -100x2 + 29x4 + -1x6 Combine like terms: x6 + -1x6 = 0 -400i2 + 116i2x2 + -4i2x4 + 0 = -100x2 + 29x4 + -1x6 -400i2 + 116i2x2 + -4i2x4 = -100x2 + 29x4 + -1x6 Reorder the terms: -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = -100x2 + 100x2 + 29x4 + -29x4 + -1x6 + x6 Combine like terms: -100x2 + 100x2 = 0 -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = 0 + 29x4 + -29x4 + -1x6 + x6 -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = 29x4 + -29x4 + -1x6 + x6 Combine like terms: 29x4 + -29x4 = 0 -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = 0 + -1x6 + x6 -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = -1x6 + x6 Combine like terms: -1x6 + x6 = 0 -400i2 + 116i2x2 + -4i2x4 + 100x2 + -29x4 + x6 = 0 The solution to this equation could not be determined.
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