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Simplifying (x + 7)(x + -11)(x + 2 + 6i)(x + 2 + -6i) = 0 Reorder the terms: (7 + x)(x + -11)(x + 2 + 6i)(x + 2 + -6i) = 0 Reorder the terms: (7 + x)(-11 + x)(x + 2 + 6i)(x + 2 + -6i) = 0 Reorder the terms: (7 + x)(-11 + x)(2 + 6i + x)(x + 2 + -6i) = 0 Reorder the terms: (7 + x)(-11 + x)(2 + 6i + x)(2 + -6i + x) = 0 Multiply (7 + x) * (-11 + x) (7(-11 + x) + x(-11 + x))(2 + 6i + x)(2 + -6i + x) = 0 ((-11 * 7 + x * 7) + x(-11 + x))(2 + 6i + x)(2 + -6i + x) = 0 ((-77 + 7x) + x(-11 + x))(2 + 6i + x)(2 + -6i + x) = 0 (-77 + 7x + (-11 * x + x * x))(2 + 6i + x)(2 + -6i + x) = 0 (-77 + 7x + (-11x + x2))(2 + 6i + x)(2 + -6i + x) = 0 Combine like terms: 7x + -11x = -4x (-77 + -4x + x2)(2 + 6i + x)(2 + -6i + x) = 0 Multiply (-77 + -4x + x2) * (2 + 6i + x) (-77(2 + 6i + x) + -4x * (2 + 6i + x) + x2(2 + 6i + x))(2 + -6i + x) = 0 ((2 * -77 + 6i * -77 + x * -77) + -4x * (2 + 6i + x) + x2(2 + 6i + x))(2 + -6i + x) = 0 ((-154 + -462i + -77x) + -4x * (2 + 6i + x) + x2(2 + 6i + x))(2 + -6i + x) = 0 (-154 + -462i + -77x + (2 * -4x + 6i * -4x + x * -4x) + x2(2 + 6i + x))(2 + -6i + x) = 0 Reorder the terms: (-154 + -462i + -77x + (-24ix + -8x + -4x2) + x2(2 + 6i + x))(2 + -6i + x) = 0 (-154 + -462i + -77x + (-24ix + -8x + -4x2) + x2(2 + 6i + x))(2 + -6i + x) = 0 (-154 + -462i + -77x + -24ix + -8x + -4x2 + (2 * x2 + 6i * x2 + x * x2))(2 + -6i + x) = 0 Reorder the terms: (-154 + -462i + -77x + -24ix + -8x + -4x2 + (6ix2 + 2x2 + x3))(2 + -6i + x) = 0 (-154 + -462i + -77x + -24ix + -8x + -4x2 + (6ix2 + 2x2 + x3))(2 + -6i + x) = 0 Reorder the terms: (-154 + -462i + -24ix + 6ix2 + -77x + -8x + -4x2 + 2x2 + x3)(2 + -6i + x) = 0 Combine like terms: -77x + -8x = -85x (-154 + -462i + -24ix + 6ix2 + -85x + -4x2 + 2x2 + x3)(2 + -6i + x) = 0 Combine like terms: -4x2 + 2x2 = -2x2 (-154 + -462i + -24ix + 6ix2 + -85x + -2x2 + x3)(2 + -6i + x) = 0 Multiply (-154 + -462i + -24ix + 6ix2 + -85x + -2x2 + x3) * (2 + -6i + x) (-154(2 + -6i + x) + -462i * (2 + -6i + x) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 ((2 * -154 + -6i * -154 + x * -154) + -462i * (2 + -6i + x) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 ((-308 + 924i + -154x) + -462i * (2 + -6i + x) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + (2 * -462i + -6i * -462i + x * -462i) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 Reorder the terms: (-308 + 924i + -154x + (-924i + -462ix + 2772i2) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + (-924i + -462ix + 2772i2) + -24ix * (2 + -6i + x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + (2 * -24ix + -6i * -24ix + x * -24ix) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 Reorder the terms: (-308 + 924i + -154x + -924i + -462ix + 2772i2 + (-48ix + -24ix2 + 144i2x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + (-48ix + -24ix2 + 144i2x) + 6ix2 * (2 + -6i + x) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + (2 * 6ix2 + -6i * 6ix2 + x * 6ix2) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 Reorder the terms: (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + (12ix2 + 6ix3 + -36i2x2) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + (12ix2 + 6ix3 + -36i2x2) + -85x * (2 + -6i + x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + (2 * -85x + -6i * -85x + x * -85x) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 Reorder the terms: (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + (510ix + -170x + -85x2) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + (510ix + -170x + -85x2) + -2x2 * (2 + -6i + x) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + (2 * -2x2 + -6i * -2x2 + x * -2x2) + x3(2 + -6i + x)) = 0 Reorder the terms: (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + (12ix2 + -4x2 + -2x3) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + (12ix2 + -4x2 + -2x3) + x3(2 + -6i + x)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + 12ix2 + -4x2 + -2x3 + (2 * x3 + -6i * x3 + x * x3)) = 0 Reorder the terms: (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + 12ix2 + -4x2 + -2x3 + (-6ix3 + 2x3 + x4)) = 0 (-308 + 924i + -154x + -924i + -462ix + 2772i2 + -48ix + -24ix2 + 144i2x + 12ix2 + 6ix3 + -36i2x2 + 510ix + -170x + -85x2 + 12ix2 + -4x2 + -2x3 + (-6ix3 + 2x3 + x4)) = 0 Reorder the terms: (-308 + 924i + -924i + -462ix + -48ix + 510ix + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: 924i + -924i = 0 (-308 + 0 + -462ix + -48ix + 510ix + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 (-308 + -462ix + -48ix + 510ix + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -462ix + -48ix = -510ix (-308 + -510ix + 510ix + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -510ix + 510ix = 0 (-308 + 0 + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 (-308 + -24ix2 + 12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -24ix2 + 12ix2 = -12ix2 (-308 + -12ix2 + 12ix2 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -12ix2 + 12ix2 = 0 (-308 + 0 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 (-308 + 6ix3 + -6ix3 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: 6ix3 + -6ix3 = 0 (-308 + 0 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 (-308 + 2772i2 + 144i2x + -36i2x2 + -154x + -170x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -154x + -170x = -324x (-308 + 2772i2 + 144i2x + -36i2x2 + -324x + -85x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -85x2 + -4x2 = -89x2 (-308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -2x3 + 2x3 = 0 (-308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + 0 + x4) = 0 (-308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4) = 0 Solving -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '308' to each side of the equation. -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + 308 + x4 = 0 + 308 Reorder the terms: -308 + 308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + 308 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + 308 Combine like terms: 0 + 308 = 308 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 308 Add '324x' to each side of the equation. 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + 324x + x4 = 308 + 324x Reorder the terms: 2772i2 + 144i2x + -36i2x2 + -324x + 324x + -89x2 + x4 = 308 + 324x Combine like terms: -324x + 324x = 0 2772i2 + 144i2x + -36i2x2 + 0 + -89x2 + x4 = 308 + 324x 2772i2 + 144i2x + -36i2x2 + -89x2 + x4 = 308 + 324x Add '89x2' to each side of the equation. 2772i2 + 144i2x + -36i2x2 + -89x2 + 89x2 + x4 = 308 + 324x + 89x2 Combine like terms: -89x2 + 89x2 = 0 2772i2 + 144i2x + -36i2x2 + 0 + x4 = 308 + 324x + 89x2 2772i2 + 144i2x + -36i2x2 + x4 = 308 + 324x + 89x2 Add '-1x4' to each side of the equation. 2772i2 + 144i2x + -36i2x2 + x4 + -1x4 = 308 + 324x + 89x2 + -1x4 Combine like terms: x4 + -1x4 = 0 2772i2 + 144i2x + -36i2x2 + 0 = 308 + 324x + 89x2 + -1x4 2772i2 + 144i2x + -36i2x2 = 308 + 324x + 89x2 + -1x4 Reorder the terms: -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 308 + 324x + 89x2 + -1x4 + -308 + -324x + -89x2 + x4 Reorder the terms: -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 308 + -308 + 324x + -324x + 89x2 + -89x2 + -1x4 + x4 Combine like terms: 308 + -308 = 0 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + 324x + -324x + 89x2 + -89x2 + -1x4 + x4 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 324x + -324x + 89x2 + -89x2 + -1x4 + x4 Combine like terms: 324x + -324x = 0 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + 89x2 + -89x2 + -1x4 + x4 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 89x2 + -89x2 + -1x4 + x4 Combine like terms: 89x2 + -89x2 = 0 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 + -1x4 + x4 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -308 + 2772i2 + 144i2x + -36i2x2 + -324x + -89x2 + x4 = 0 The solution to this equation could not be determined.
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