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Simplifying (x + -2)(x + -1(1 + i))(1 + -1(1 + -1i)) = 0 Reorder the terms: (-2 + x)(x + -1(1 + i))(1 + -1(1 + -1i)) = 0 (-2 + x)(x + (1 * -1 + i * -1))(1 + -1(1 + -1i)) = 0 (-2 + x)(x + (-1 + -1i))(1 + -1(1 + -1i)) = 0 Reorder the terms: (-2 + x)(-1 + -1i + x)(1 + -1(1 + -1i)) = 0 (-2 + x)(-1 + -1i + x)(1 + (1 * -1 + -1i * -1)) = 0 (-2 + x)(-1 + -1i + x)(1 + (-1 + 1i)) = 0 Combine like terms: 1 + -1 = 0 (-2 + x)(-1 + -1i + x)(0 + 1i) = 0 (-2 + x)(-1 + -1i + x)(1i) = 0 Remove parenthesis around (1i) (-2 + x)(-1 + -1i + x) * 1i = 0 Reorder the terms for easier multiplication: 1i(-2 + x)(-1 + -1i + x) = 0 Multiply (-2 + x) * (-1 + -1i + x) 1i(-2(-1 + -1i + x) + x(-1 + -1i + x)) = 0 1i((-1 * -2 + -1i * -2 + x * -2) + x(-1 + -1i + x)) = 0 1i((2 + 2i + -2x) + x(-1 + -1i + x)) = 0 1i(2 + 2i + -2x + (-1 * x + -1i * x + x * x)) = 0 Reorder the terms: 1i(2 + 2i + -2x + (-1ix + -1x + x2)) = 0 1i(2 + 2i + -2x + (-1ix + -1x + x2)) = 0 Reorder the terms: 1i(2 + 2i + -1ix + -2x + -1x + x2) = 0 Combine like terms: -2x + -1x = -3x 1i(2 + 2i + -1ix + -3x + x2) = 0 (2 * 1i + 2i * 1i + -1ix * 1i + -3x * 1i + x2 * 1i) = 0 Reorder the terms: (2i + -3ix + 1ix2 + 2i2 + -1i2x) = 0 (2i + -3ix + 1ix2 + 2i2 + -1i2x) = 0 Solving 2i + -3ix + 1ix2 + 2i2 + -1i2x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'i'. i(2 + -3x + x2 + 2i + -1ix) = 0Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(2 + -3x + x2 + 2i + -1ix)' equal to zero and attempt to solve: Simplifying 2 + -3x + x2 + 2i + -1ix = 0 Reorder the terms: 2 + 2i + -1ix + -3x + x2 = 0 Solving 2 + 2i + -1ix + -3x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 2i + -1ix + -3x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2i + -1ix + -3x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2i + -1ix + -3x + x2 = 0 + -2 2i + -1ix + -3x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2i + -1ix + -3x + x2 = -2 Add '3x' to each side of the equation. 2i + -1ix + -3x + 3x + x2 = -2 + 3x Combine like terms: -3x + 3x = 0 2i + -1ix + 0 + x2 = -2 + 3x 2i + -1ix + x2 = -2 + 3x Add '-1x2' to each side of the equation. 2i + -1ix + x2 + -1x2 = -2 + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 2i + -1ix + 0 = -2 + 3x + -1x2 2i + -1ix = -2 + 3x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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