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Simplifying x(x + 2i)(x + -2i)[x + -1(2 + i)][x + -1(2 + -1i)] = 0 Reorder the terms: x(2i + x)(x + -2i)[x + -1(2 + i)][x + -1(2 + -1i)] = 0 Reorder the terms: x(2i + x)(-2i + x)[x + -1(2 + i)][x + -1(2 + -1i)] = 0 x(2i + x)(-2i + x)[x + (2 * -1 + i * -1)][x + -1(2 + -1i)] = 0 x(2i + x)(-2i + x)[x + (-2 + -1i)][x + -1(2 + -1i)] = 0 Reorder the terms: x(2i + x)(-2i + x)[-2 + -1i + x][x + -1(2 + -1i)] = 0 x(2i + x)(-2i + x)[-2 + -1i + x][x + (2 * -1 + -1i * -1)] = 0 x(2i + x)(-2i + x)[-2 + -1i + x][x + (-2 + 1i)] = 0 Reorder the terms: x(2i + x)(-2i + x)[-2 + -1i + x][-2 + 1i + x] = 0 Multiply (2i + x) * (-2i + x) x(2i * (-2i + x) + x(-2i + x))[-2 + -1i + x][-2 + 1i + x] = 0 x((-2i * 2i + x * 2i) + x(-2i + x))[-2 + -1i + x][-2 + 1i + x] = 0 Reorder the terms: x((2ix + -4i2) + x(-2i + x))[-2 + -1i + x][-2 + 1i + x] = 0 x((2ix + -4i2) + x(-2i + x))[-2 + -1i + x][-2 + 1i + x] = 0 x(2ix + -4i2 + (-2i * x + x * x))[-2 + -1i + x][-2 + 1i + x] = 0 x(2ix + -4i2 + (-2ix + x2))[-2 + -1i + x][-2 + 1i + x] = 0 Reorder the terms: x(2ix + -2ix + -4i2 + x2)[-2 + -1i + x][-2 + 1i + x] = 0 Combine like terms: 2ix + -2ix = 0 x(0 + -4i2 + x2)[-2 + -1i + x][-2 + 1i + x] = 0 x(-4i2 + x2)[-2 + -1i + x][-2 + 1i + x] = 0 Multiply (-4i2 + x2) * [-2 + -1i + x] x(-4i2 * [-2 + -1i + x] + x2[-2 + -1i + x])[-2 + 1i + x] = 0 x([-2 * -4i2 + -1i * -4i2 + x * -4i2] + x2[-2 + -1i + x])[-2 + 1i + x] = 0 Reorder the terms: x([8i2 + -4i2x + 4i3] + x2[-2 + -1i + x])[-2 + 1i + x] = 0 x([8i2 + -4i2x + 4i3] + x2[-2 + -1i + x])[-2 + 1i + x] = 0 x(8i2 + -4i2x + 4i3 + [-2 * x2 + -1i * x2 + x * x2])[-2 + 1i + x] = 0 Reorder the terms: x(8i2 + -4i2x + 4i3 + [-1ix2 + -2x2 + x3])[-2 + 1i + x] = 0 x(8i2 + -4i2x + 4i3 + [-1ix2 + -2x2 + x3])[-2 + 1i + x] = 0 Reorder the terms: x(-1ix2 + 8i2 + -4i2x + 4i3 + -2x2 + x3)[-2 + 1i + x] = 0 x(-1ix2 + 8i2 + -4i2x + 4i3 + -2x2 + x3)[-2 + 1i + x] = 0 Multiply (-1ix2 + 8i2 + -4i2x + 4i3 + -2x2 + x3) * [-2 + 1i + x] x(-1ix2 * [-2 + 1i + x] + 8i2 * [-2 + 1i + x] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x([-2 * -1ix2 + 1i * -1ix2 + x * -1ix2] + 8i2 * [-2 + 1i + x] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 Reorder the terms: x([2ix2 + -1ix3 + -1i2x2] + 8i2 * [-2 + 1i + x] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x([2ix2 + -1ix3 + -1i2x2] + 8i2 * [-2 + 1i + x] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + [-2 * 8i2 + 1i * 8i2 + x * 8i2] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 Reorder the terms: x(2ix2 + -1ix3 + -1i2x2 + [-16i2 + 8i2x + 8i3] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + [-16i2 + 8i2x + 8i3] + -4i2x * [-2 + 1i + x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + [-2 * -4i2x + 1i * -4i2x + x * -4i2x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 Reorder the terms: x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + [8i2x + -4i2x2 + -4i3x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + [8i2x + -4i2x2 + -4i3x] + 4i3 * [-2 + 1i + x] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + [-2 * 4i3 + 1i * 4i3 + x * 4i3] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 Reorder the terms: x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + [-8i3 + 4i3x + 4i4] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + [-8i3 + 4i3x + 4i4] + -2x2 * [-2 + 1i + x] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + [-2 * -2x2 + 1i * -2x2 + x * -2x2] + x3[-2 + 1i + x]) = 0 Reorder the terms: x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + [-2ix2 + 4x2 + -2x3] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + [-2ix2 + 4x2 + -2x3] + x3[-2 + 1i + x]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + -2ix2 + 4x2 + -2x3 + [-2 * x3 + 1i * x3 + x * x3]) = 0 Reorder the terms: x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + -2ix2 + 4x2 + -2x3 + [1ix3 + -2x3 + x4]) = 0 x(2ix2 + -1ix3 + -1i2x2 + -16i2 + 8i2x + 8i3 + 8i2x + -4i2x2 + -4i3x + -8i3 + 4i3x + 4i4 + -2ix2 + 4x2 + -2x3 + [1ix3 + -2x3 + x4]) = 0 Reorder the terms: x(2ix2 + -2ix2 + -1ix3 + 1ix3 + -16i2 + 8i2x + 8i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: 2ix2 + -2ix2 = 0 x(0 + -1ix3 + 1ix3 + -16i2 + 8i2x + 8i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 x(-1ix3 + 1ix3 + -16i2 + 8i2x + 8i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: -1ix3 + 1ix3 = 0 x(0 + -16i2 + 8i2x + 8i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 x(-16i2 + 8i2x + 8i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: 8i2x + 8i2x = 16i2x x(-16i2 + 16i2x + -1i2x2 + -4i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: -1i2x2 + -4i2x2 = -5i2x2 x(-16i2 + 16i2x + -5i2x2 + 8i3 + -8i3 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: 8i3 + -8i3 = 0 x(-16i2 + 16i2x + -5i2x2 + 0 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 x(-16i2 + 16i2x + -5i2x2 + -4i3x + 4i3x + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: -4i3x + 4i3x = 0 x(-16i2 + 16i2x + -5i2x2 + 0 + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 x(-16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -2x3 + -2x3 + x4) = 0 Combine like terms: -2x3 + -2x3 = -4x3 x(-16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -4x3 + x4) = 0 (-16i2 * x + 16i2x * x + -5i2x2 * x + 4i4 * x + 4x2 * x + -4x3 * x + x4 * x) = 0 (-16i2x + 16i2x2 + -5i2x3 + 4i4x + 4x3 + -4x4 + x5) = 0 Solving -16i2x + 16i2x2 + -5i2x3 + 4i4x + 4x3 + -4x4 + x5 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'x'. x(-16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -4x3 + x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -4x3 + x4)' equal to zero and attempt to solve: Simplifying -16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -4x3 + x4 = 0 Solving -16i2 + 16i2x + -5i2x2 + 4i4 + 4x2 + -4x3 + x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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