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Simplifying (x(1 + -1i))(x(1 + i))(x + -2) = 0 ((1 * x + -1i * x))(x(1 + i))(x + -2) = 0 Reorder the terms: ((-1ix + 1x))(x(1 + i))(x + -2) = 0 ((-1ix + 1x))(x(1 + i))(x + -2) = 0 (-1ix + 1x)((1 * x + i * x))(x + -2) = 0 Reorder the terms: (-1ix + 1x)((ix + 1x))(x + -2) = 0 (-1ix + 1x)((ix + 1x))(x + -2) = 0 Reorder the terms: (-1ix + 1x)(ix + 1x)(-2 + x) = 0 Multiply (-1ix + 1x) * (ix + 1x) (-1ix * (ix + 1x) + 1x * (ix + 1x))(-2 + x) = 0 ((ix * -1ix + 1x * -1ix) + 1x * (ix + 1x))(-2 + x) = 0 Reorder the terms: ((-1ix2 + -1i2x2) + 1x * (ix + 1x))(-2 + x) = 0 ((-1ix2 + -1i2x2) + 1x * (ix + 1x))(-2 + x) = 0 (-1ix2 + -1i2x2 + (ix * 1x + 1x * 1x))(-2 + x) = 0 (-1ix2 + -1i2x2 + (1ix2 + 1x2))(-2 + x) = 0 Reorder the terms: (-1ix2 + 1ix2 + -1i2x2 + 1x2)(-2 + x) = 0 Combine like terms: -1ix2 + 1ix2 = 0 (0 + -1i2x2 + 1x2)(-2 + x) = 0 (-1i2x2 + 1x2)(-2 + x) = 0 Multiply (-1i2x2 + 1x2) * (-2 + x) (-1i2x2 * (-2 + x) + 1x2 * (-2 + x)) = 0 ((-2 * -1i2x2 + x * -1i2x2) + 1x2 * (-2 + x)) = 0 ((2i2x2 + -1i2x3) + 1x2 * (-2 + x)) = 0 (2i2x2 + -1i2x3 + (-2 * 1x2 + x * 1x2)) = 0 (2i2x2 + -1i2x3 + (-2x2 + 1x3)) = 0 (2i2x2 + -1i2x3 + -2x2 + 1x3) = 0 Solving 2i2x2 + -1i2x3 + -2x2 + 1x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2x2' to each side of the equation. 2i2x2 + -1i2x3 + -2x2 + 2x2 + 1x3 = 0 + 2x2 Combine like terms: -2x2 + 2x2 = 0 2i2x2 + -1i2x3 + 0 + 1x3 = 0 + 2x2 2i2x2 + -1i2x3 + 1x3 = 0 + 2x2 Remove the zero: 2i2x2 + -1i2x3 + 1x3 = 2x2 Add '-1x3' to each side of the equation. 2i2x2 + -1i2x3 + 1x3 + -1x3 = 2x2 + -1x3 Combine like terms: 1x3 + -1x3 = 0 2i2x2 + -1i2x3 + 0 = 2x2 + -1x3 2i2x2 + -1i2x3 = 2x2 + -1x3 Reorder the terms: 2i2x2 + -1i2x3 + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3 Combine like terms: 2x2 + -2x2 = 0 2i2x2 + -1i2x3 + -2x2 + x3 = 0 + -1x3 + x3 2i2x2 + -1i2x3 + -2x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 2i2x2 + -1i2x3 + -2x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(2i2 + -1i2x + -2 + x) = 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 '(2i2 + -1i2x + -2 + x)' equal to zero and attempt to solve: Simplifying 2i2 + -1i2x + -2 + x = 0 Reorder the terms: -2 + 2i2 + -1i2x + x = 0 Solving -2 + 2i2 + -1i2x + x = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2i2 + -1i2x + 2 + x = 0 + 2 Reorder the terms: -2 + 2 + 2i2 + -1i2x + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2i2 + -1i2x + x = 0 + 2 2i2 + -1i2x + x = 0 + 2 Combine like terms: 0 + 2 = 2 2i2 + -1i2x + x = 2 Add '-1x' to each side of the equation. 2i2 + -1i2x + x + -1x = 2 + -1x Combine like terms: x + -1x = 0 2i2 + -1i2x + 0 = 2 + -1x 2i2 + -1i2x = 2 + -1x 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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