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Simplifying x2(x + -3)(x + -1i)[x + -1(2 + -1i)][x + (2 + -1i)] = 0 Reorder the terms: x2(-3 + x)(x + -1i)[x + -1(2 + -1i)][x + (2 + -1i)] = 0 Reorder the terms: x2(-3 + x)(-1i + x)[x + -1(2 + -1i)][x + (2 + -1i)] = 0 x2(-3 + x)(-1i + x)[x + (2 * -1 + -1i * -1)][x + (2 + -1i)] = 0 x2(-3 + x)(-1i + x)[x + (-2 + 1i)][x + (2 + -1i)] = 0 Reorder the terms: x2(-3 + x)(-1i + x)[-2 + 1i + x][x + (2 + -1i)] = 0 Remove parenthesis around (2 + -1i) x2(-3 + x)(-1i + x)[-2 + 1i + x][x + 2 + -1i] = 0 Reorder the terms: x2(-3 + x)(-1i + x)[-2 + 1i + x][2 + -1i + x] = 0 Multiply (-3 + x) * (-1i + x) x2(-3(-1i + x) + x(-1i + x))[-2 + 1i + x][2 + -1i + x] = 0 x2((-1i * -3 + x * -3) + x(-1i + x))[-2 + 1i + x][2 + -1i + x] = 0 x2((3i + -3x) + x(-1i + x))[-2 + 1i + x][2 + -1i + x] = 0 x2(3i + -3x + (-1i * x + x * x))[-2 + 1i + x][2 + -1i + x] = 0 x2(3i + -3x + (-1ix + x2))[-2 + 1i + x][2 + -1i + x] = 0 Reorder the terms: x2(3i + -1ix + -3x + x2)[-2 + 1i + x][2 + -1i + x] = 0 x2(3i + -1ix + -3x + x2)[-2 + 1i + x][2 + -1i + x] = 0 Multiply (3i + -1ix + -3x + x2) * [-2 + 1i + x] x2(3i * [-2 + 1i + x] + -1ix * [-2 + 1i + x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2([-2 * 3i + 1i * 3i + x * 3i] + -1ix * [-2 + 1i + x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 Reorder the terms: x2([-6i + 3ix + 3i2] + -1ix * [-2 + 1i + x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2([-6i + 3ix + 3i2] + -1ix * [-2 + 1i + x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + [-2 * -1ix + 1i * -1ix + x * -1ix] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 Reorder the terms: x2(-6i + 3ix + 3i2 + [2ix + -1ix2 + -1i2x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + [2ix + -1ix2 + -1i2x] + -3x * [-2 + 1i + x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + [-2 * -3x + 1i * -3x + x * -3x] + x2[-2 + 1i + x])[2 + -1i + x] = 0 Reorder the terms: x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + [-3ix + 6x + -3x2] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + [-3ix + 6x + -3x2] + x2[-2 + 1i + x])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + [-2 * x2 + 1i * x2 + x * x2])[2 + -1i + x] = 0 Reorder the terms: x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + [1ix2 + -2x2 + x3])[2 + -1i + x] = 0 x2(-6i + 3ix + 3i2 + 2ix + -1ix2 + -1i2x + -3ix + 6x + -3x2 + [1ix2 + -2x2 + x3])[2 + -1i + x] = 0 Reorder the terms: x2(-6i + 3ix + 2ix + -3ix + -1ix2 + 1ix2 + 3i2 + -1i2x + 6x + -3x2 + -2x2 + x3)[2 + -1i + x] = 0 Combine like terms: 3ix + 2ix = 5ix x2(-6i + 5ix + -3ix + -1ix2 + 1ix2 + 3i2 + -1i2x + 6x + -3x2 + -2x2 + x3)[2 + -1i + x] = 0 Combine like terms: 5ix + -3ix = 2ix x2(-6i + 2ix + -1ix2 + 1ix2 + 3i2 + -1i2x + 6x + -3x2 + -2x2 + x3)[2 + -1i + x] = 0 Combine like terms: -1ix2 + 1ix2 = 0 x2(-6i + 2ix + 0 + 3i2 + -1i2x + 6x + -3x2 + -2x2 + x3)[2 + -1i + x] = 0 x2(-6i + 2ix + 3i2 + -1i2x + 6x + -3x2 + -2x2 + x3)[2 + -1i + x] = 0 Combine like terms: -3x2 + -2x2 = -5x2 x2(-6i + 2ix + 3i2 + -1i2x + 6x + -5x2 + x3)[2 + -1i + x] = 0 Multiply (-6i + 2ix + 3i2 + -1i2x + 6x + -5x2 + x3) * [2 + -1i + x] x2(-6i * [2 + -1i + x] + 2ix * [2 + -1i + x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2([2 * -6i + -1i * -6i + x * -6i] + 2ix * [2 + -1i + x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 Reorder the terms: x2([-12i + -6ix + 6i2] + 2ix * [2 + -1i + x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2([-12i + -6ix + 6i2] + 2ix * [2 + -1i + x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + [2 * 2ix + -1i * 2ix + x * 2ix] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + [4ix + 2ix2 + -2i2x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + [4ix + 2ix2 + -2i2x] + 3i2 * [2 + -1i + x] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + [2 * 3i2 + -1i * 3i2 + x * 3i2] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + [6i2 + 3i2x + -3i3] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + [6i2 + 3i2x + -3i3] + -1i2x * [2 + -1i + x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + [2 * -1i2x + -1i * -1i2x + x * -1i2x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + [-2i2x + -1i2x2 + 1i3x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + [-2i2x + -1i2x2 + 1i3x] + 6x * [2 + -1i + x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + [2 * 6x + -1i * 6x + x * 6x] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + [-6ix + 12x + 6x2] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + [-6ix + 12x + 6x2] + -5x2 * [2 + -1i + x] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + [2 * -5x2 + -1i * -5x2 + x * -5x2] + x3[2 + -1i + x]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + [5ix2 + -10x2 + -5x3] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + [5ix2 + -10x2 + -5x3] + x3[2 + -1i + x]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + 5ix2 + -10x2 + -5x3 + [2 * x3 + -1i * x3 + x * x3]) = 0 Reorder the terms: x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + 5ix2 + -10x2 + -5x3 + [-1ix3 + 2x3 + x4]) = 0 x2(-12i + -6ix + 6i2 + 4ix + 2ix2 + -2i2x + 6i2 + 3i2x + -3i3 + -2i2x + -1i2x2 + 1i3x + -6ix + 12x + 6x2 + 5ix2 + -10x2 + -5x3 + [-1ix3 + 2x3 + x4]) = 0 Reorder the terms: x2(-12i + -6ix + 4ix + -6ix + 2ix2 + 5ix2 + -1ix3 + 6i2 + 6i2 + -2i2x + 3i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: -6ix + 4ix = -2ix x2(-12i + -2ix + -6ix + 2ix2 + 5ix2 + -1ix3 + 6i2 + 6i2 + -2i2x + 3i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: -2ix + -6ix = -8ix x2(-12i + -8ix + 2ix2 + 5ix2 + -1ix3 + 6i2 + 6i2 + -2i2x + 3i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: 2ix2 + 5ix2 = 7ix2 x2(-12i + -8ix + 7ix2 + -1ix3 + 6i2 + 6i2 + -2i2x + 3i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: 6i2 + 6i2 = 12i2 x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -2i2x + 3i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: -2i2x + 3i2x = 1i2x x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + 1i2x + -2i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: 1i2x + -2i2x = -1i2x x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + 1i3x + 12x + 6x2 + -10x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: 6x2 + -10x2 = -4x2 x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + 1i3x + 12x + -4x2 + -5x3 + 2x3 + x4) = 0 Combine like terms: -5x3 + 2x3 = -3x3 x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + 1i3x + 12x + -4x2 + -3x3 + x4) = 0 (-12i * x2 + -8ix * x2 + 7ix2 * x2 + -1ix3 * x2 + 12i2 * x2 + -1i2x * x2 + -1i2x2 * x2 + -3i3 * x2 + 1i3x * x2 + 12x * x2 + -4x2 * x2 + -3x3 * x2 + x4 * x2) = 0 (-12ix2 + -8ix3 + 7ix4 + -1ix5 + 12i2x2 + -1i2x3 + -1i2x4 + -3i3x2 + 1i3x3 + 12x3 + -4x4 + -3x5 + x6) = 0 Solving -12ix2 + -8ix3 + 7ix4 + -1ix5 + 12i2x2 + -1i2x3 + -1i2x4 + -3i3x2 + 1i3x3 + 12x3 + -4x4 + -3x5 + x6 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + i3x + 12x + -4x2 + -3x3 + x4) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 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 '(-12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + i3x + 12x + -4x2 + -3x3 + x4)' equal to zero and attempt to solve: Simplifying -12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + i3x + 12x + -4x2 + -3x3 + x4 = 0 Solving -12i + -8ix + 7ix2 + -1ix3 + 12i2 + -1i2x + -1i2x2 + -3i3 + i3x + 12x + -4x2 + -3x3 + 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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