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Simplifying x(x + -1)(x + -1 + -1i)(x + -1 + i) = f(x) Reorder the terms: x(-1 + x)(x + -1 + -1i)(x + -1 + i) = f(x) Reorder the terms: x(-1 + x)(-1 + -1i + x)(x + -1 + i) = f(x) Reorder the terms: x(-1 + x)(-1 + -1i + x)(-1 + i + x) = f(x) Multiply (-1 + x) * (-1 + -1i + x) x(-1(-1 + -1i + x) + x(-1 + -1i + x))(-1 + i + x) = f(x) x((-1 * -1 + -1i * -1 + x * -1) + x(-1 + -1i + x))(-1 + i + x) = f(x) x((1 + 1i + -1x) + x(-1 + -1i + x))(-1 + i + x) = f(x) x(1 + 1i + -1x + (-1 * x + -1i * x + x * x))(-1 + i + x) = f(x) Reorder the terms: x(1 + 1i + -1x + (-1ix + -1x + x2))(-1 + i + x) = f(x) x(1 + 1i + -1x + (-1ix + -1x + x2))(-1 + i + x) = f(x) Reorder the terms: x(1 + 1i + -1ix + -1x + -1x + x2)(-1 + i + x) = f(x) Combine like terms: -1x + -1x = -2x x(1 + 1i + -1ix + -2x + x2)(-1 + i + x) = f(x) Multiply (1 + 1i + -1ix + -2x + x2) * (-1 + i + x) x(1(-1 + i + x) + 1i * (-1 + i + x) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x((-1 * 1 + i * 1 + x * 1) + 1i * (-1 + i + x) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x((-1 + 1i + 1x) + 1i * (-1 + i + x) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + (-1 * 1i + i * 1i + x * 1i) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) Reorder the terms: x(-1 + 1i + 1x + (-1i + 1ix + 1i2) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + (-1i + 1ix + 1i2) + -1ix * (-1 + i + x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + (-1 * -1ix + i * -1ix + x * -1ix) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) Reorder the terms: x(-1 + 1i + 1x + -1i + 1ix + 1i2 + (1ix + -1ix2 + -1i2x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + (1ix + -1ix2 + -1i2x) + -2x * (-1 + i + x) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + (-1 * -2x + i * -2x + x * -2x) + x2(-1 + i + x)) = f(x) Reorder the terms: x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + (-2ix + 2x + -2x2) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + (-2ix + 2x + -2x2) + x2(-1 + i + x)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + -2ix + 2x + -2x2 + (-1 * x2 + i * x2 + x * x2)) = f(x) Reorder the terms: x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + -2ix + 2x + -2x2 + (ix2 + -1x2 + x3)) = f(x) x(-1 + 1i + 1x + -1i + 1ix + 1i2 + 1ix + -1ix2 + -1i2x + -2ix + 2x + -2x2 + (ix2 + -1x2 + x3)) = f(x) Reorder the terms: x(-1 + 1i + -1i + 1ix + 1ix + -2ix + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) Combine like terms: 1i + -1i = 0 x(-1 + 0 + 1ix + 1ix + -2ix + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) x(-1 + 1ix + 1ix + -2ix + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) Combine like terms: 1ix + 1ix = 2ix x(-1 + 2ix + -2ix + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) Combine like terms: 2ix + -2ix = 0 x(-1 + 0 + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) x(-1 + -1ix2 + ix2 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) Combine like terms: -1ix2 + ix2 = 0 x(-1 + 0 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) x(-1 + 1i2 + -1i2x + 1x + 2x + -2x2 + -1x2 + x3) = f(x) Combine like terms: 1x + 2x = 3x x(-1 + 1i2 + -1i2x + 3x + -2x2 + -1x2 + x3) = f(x) Combine like terms: -2x2 + -1x2 = -3x2 x(-1 + 1i2 + -1i2x + 3x + -3x2 + x3) = f(x) (-1 * x + 1i2 * x + -1i2x * x + 3x * x + -3x2 * x + x3 * x) = f(x) Reorder the terms: (1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4) = f(x) (1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4) = f(x) Multiply f * x 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = fx Solving 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = fx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x + x4 = fx + x Reorder the terms: 1i2x + -1i2x2 + -1x + x + 3x2 + -3x3 + x4 = fx + x Combine like terms: -1x + x = 0 1i2x + -1i2x2 + 0 + 3x2 + -3x3 + x4 = fx + x 1i2x + -1i2x2 + 3x2 + -3x3 + x4 = fx + x Add '-3x2' to each side of the equation. 1i2x + -1i2x2 + 3x2 + -3x3 + -3x2 + x4 = fx + x + -3x2 Reorder the terms: 1i2x + -1i2x2 + 3x2 + -3x2 + -3x3 + x4 = fx + x + -3x2 Combine like terms: 3x2 + -3x2 = 0 1i2x + -1i2x2 + 0 + -3x3 + x4 = fx + x + -3x2 1i2x + -1i2x2 + -3x3 + x4 = fx + x + -3x2 Add '3x3' to each side of the equation. 1i2x + -1i2x2 + -3x3 + 3x3 + x4 = fx + x + -3x2 + 3x3 Combine like terms: -3x3 + 3x3 = 0 1i2x + -1i2x2 + 0 + x4 = fx + x + -3x2 + 3x3 1i2x + -1i2x2 + x4 = fx + x + -3x2 + 3x3 Add '-1x4' to each side of the equation. 1i2x + -1i2x2 + x4 + -1x4 = fx + x + -3x2 + 3x3 + -1x4 Combine like terms: x4 + -1x4 = 0 1i2x + -1i2x2 + 0 = fx + x + -3x2 + 3x3 + -1x4 1i2x + -1i2x2 = fx + x + -3x2 + 3x3 + -1x4 Reorder the terms: -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = fx + x + -3x2 + 3x3 + -1x4 + -1fx + -1x + 3x2 + -3x3 + x4 Reorder the terms: -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = fx + -1fx + x + -1x + -3x2 + 3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: fx + -1fx = 0 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 0 + x + -1x + -3x2 + 3x2 + 3x3 + -3x3 + -1x4 + x4 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = x + -1x + -3x2 + 3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: x + -1x = 0 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 0 + -3x2 + 3x2 + 3x3 + -3x3 + -1x4 + x4 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = -3x2 + 3x2 + 3x3 + -3x3 + -1x4 + x4 Combine like terms: -3x2 + 3x2 = 0 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 0 + 3x3 + -3x3 + -1x4 + x4 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 3x3 + -3x3 + -1x4 + x4 Combine like terms: 3x3 + -3x3 = 0 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 0 + -1x4 + x4 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -1fx + 1i2x + -1i2x2 + -1x + 3x2 + -3x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1f + i2 + -1i2x + -1 + 3x + -3x2 + x3) = 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 '(-1f + i2 + -1i2x + -1 + 3x + -3x2 + x3)' equal to zero and attempt to solve: Simplifying -1f + i2 + -1i2x + -1 + 3x + -3x2 + x3 = 0 Reorder the terms: -1 + -1f + i2 + -1i2x + 3x + -3x2 + x3 = 0 Solving -1 + -1f + i2 + -1i2x + 3x + -3x2 + x3 = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1f + i2 + -1i2x + 3x + -3x2 + 1 + x3 = 0 + 1 Reorder the terms: -1 + 1 + -1f + i2 + -1i2x + 3x + -3x2 + x3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1f + i2 + -1i2x + 3x + -3x2 + x3 = 0 + 1 -1f + i2 + -1i2x + 3x + -3x2 + x3 = 0 + 1 Combine like terms: 0 + 1 = 1 -1f + i2 + -1i2x + 3x + -3x2 + x3 = 1 Add 'f' to each side of the equation. -1f + i2 + -1i2x + 3x + -3x2 + f + x3 = 1 + f Reorder the terms: -1f + f + i2 + -1i2x + 3x + -3x2 + x3 = 1 + f Combine like terms: -1f + f = 0 0 + i2 + -1i2x + 3x + -3x2 + x3 = 1 + f i2 + -1i2x + 3x + -3x2 + x3 = 1 + f Add '-3x' to each side of the equation. i2 + -1i2x + 3x + -3x2 + -3x + x3 = 1 + f + -3x Reorder the terms: i2 + -1i2x + 3x + -3x + -3x2 + x3 = 1 + f + -3x Combine like terms: 3x + -3x = 0 i2 + -1i2x + 0 + -3x2 + x3 = 1 + f + -3x i2 + -1i2x + -3x2 + x3 = 1 + f + -3x Add '3x2' to each side of the equation. i2 + -1i2x + -3x2 + 3x2 + x3 = 1 + f + -3x + 3x2 Combine like terms: -3x2 + 3x2 = 0 i2 + -1i2x + 0 + x3 = 1 + f + -3x + 3x2 i2 + -1i2x + x3 = 1 + f + -3x + 3x2 Add '-1x3' to each side of the equation. i2 + -1i2x + x3 + -1x3 = 1 + f + -3x + 3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 i2 + -1i2x + 0 = 1 + f + -3x + 3x2 + -1x3 i2 + -1i2x = 1 + f + -3x + 3x2 + -1x3 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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