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Simplifying x3 + -1(3 + i) * x2 + (4 + 3i) * x = 0 Reorder the terms for easier multiplication: x3 + -1x2(3 + i) + (4 + 3i) * x = 0 x3 + (3 * -1x2 + i * -1x2) + (4 + 3i) * x = 0 Reorder the terms: x3 + (-1ix2 + -3x2) + (4 + 3i) * x = 0 x3 + (-1ix2 + -3x2) + (4 + 3i) * x = 0 Reorder the terms for easier multiplication: x3 + -1ix2 + -3x2 + x(4 + 3i) = 0 x3 + -1ix2 + -3x2 + (4 * x + 3i * x) = 0 Reorder the terms: x3 + -1ix2 + -3x2 + (3ix + 4x) = 0 x3 + -1ix2 + -3x2 + (3ix + 4x) = 0 Reorder the terms: 3ix + -1ix2 + 4x + -3x2 + x3 = 0 Solving 3ix + -1ix2 + 4x + -3x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4x' to each side of the equation. 3ix + -1ix2 + 4x + -3x2 + -4x + x3 = 0 + -4x Reorder the terms: 3ix + -1ix2 + 4x + -4x + -3x2 + x3 = 0 + -4x Combine like terms: 4x + -4x = 0 3ix + -1ix2 + 0 + -3x2 + x3 = 0 + -4x 3ix + -1ix2 + -3x2 + x3 = 0 + -4x Remove the zero: 3ix + -1ix2 + -3x2 + x3 = -4x Add '3x2' to each side of the equation. 3ix + -1ix2 + -3x2 + 3x2 + x3 = -4x + 3x2 Combine like terms: -3x2 + 3x2 = 0 3ix + -1ix2 + 0 + x3 = -4x + 3x2 3ix + -1ix2 + x3 = -4x + 3x2 Add '-1x3' to each side of the equation. 3ix + -1ix2 + x3 + -1x3 = -4x + 3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 3ix + -1ix2 + 0 = -4x + 3x2 + -1x3 3ix + -1ix2 = -4x + 3x2 + -1x3 Reorder the terms: 3ix + -1ix2 + 4x + -3x2 + x3 = -4x + 4x + 3x2 + -3x2 + -1x3 + x3 Combine like terms: -4x + 4x = 0 3ix + -1ix2 + 4x + -3x2 + x3 = 0 + 3x2 + -3x2 + -1x3 + x3 3ix + -1ix2 + 4x + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3 Combine like terms: 3x2 + -3x2 = 0 3ix + -1ix2 + 4x + -3x2 + x3 = 0 + -1x3 + x3 3ix + -1ix2 + 4x + -3x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3ix + -1ix2 + 4x + -3x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3i + -1ix + 4 + -3x + x2) = 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 '(3i + -1ix + 4 + -3x + x2)' equal to zero and attempt to solve: Simplifying 3i + -1ix + 4 + -3x + x2 = 0 Reorder the terms: 4 + 3i + -1ix + -3x + x2 = 0 Solving 4 + 3i + -1ix + -3x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 3i + -1ix + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 3i + -1ix + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i + -1ix + -3x + x2 = 0 + -4 3i + -1ix + -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 3i + -1ix + -3x + x2 = -4 Add '3x' to each side of the equation. 3i + -1ix + -3x + 3x + x2 = -4 + 3x Combine like terms: -3x + 3x = 0 3i + -1ix + 0 + x2 = -4 + 3x 3i + -1ix + x2 = -4 + 3x Add '-1x2' to each side of the equation. 3i + -1ix + x2 + -1x2 = -4 + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 3i + -1ix + 0 = -4 + 3x + -1x2 3i + -1ix = -4 + 3x + -1x2 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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