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Simplifying (x + 1)[x + -1(5 + 3i)] = 0 Reorder the terms: (1 + x)[x + -1(5 + 3i)] = 0 (1 + x)[x + (5 * -1 + 3i * -1)] = 0 (1 + x)[x + (-5 + -3i)] = 0 Reorder the terms: (1 + x)[-5 + -3i + x] = 0 Multiply (1 + x) * [-5 + -3i + x] (1[-5 + -3i + x] + x[-5 + -3i + x]) = 0 ([-5 * 1 + -3i * 1 + x * 1] + x[-5 + -3i + x]) = 0 ([-5 + -3i + 1x] + x[-5 + -3i + x]) = 0 (-5 + -3i + 1x + [-5 * x + -3i * x + x * x]) = 0 Reorder the terms: (-5 + -3i + 1x + [-3ix + -5x + x2]) = 0 (-5 + -3i + 1x + [-3ix + -5x + x2]) = 0 Reorder the terms: (-5 + -3i + -3ix + 1x + -5x + x2) = 0 Combine like terms: 1x + -5x = -4x (-5 + -3i + -3ix + -4x + x2) = 0 Solving -5 + -3i + -3ix + -4x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -3i + -3ix + -4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -3i + -3ix + -4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3i + -3ix + -4x + x2 = 0 + 5 -3i + -3ix + -4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -3i + -3ix + -4x + x2 = 5 Add '4x' to each side of the equation. -3i + -3ix + -4x + 4x + x2 = 5 + 4x Combine like terms: -4x + 4x = 0 -3i + -3ix + 0 + x2 = 5 + 4x -3i + -3ix + x2 = 5 + 4x Add '-1x2' to each side of the equation. -3i + -3ix + x2 + -1x2 = 5 + 4x + -1x2 Combine like terms: x2 + -1x2 = 0 -3i + -3ix + 0 = 5 + 4x + -1x2 -3i + -3ix = 5 + 4x + -1x2 Reorder the terms: -5 + -3i + -3ix + -4x + x2 = 5 + 4x + -1x2 + -5 + -4x + x2 Reorder the terms: -5 + -3i + -3ix + -4x + x2 = 5 + -5 + 4x + -4x + -1x2 + x2 Combine like terms: 5 + -5 = 0 -5 + -3i + -3ix + -4x + x2 = 0 + 4x + -4x + -1x2 + x2 -5 + -3i + -3ix + -4x + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 -5 + -3i + -3ix + -4x + x2 = 0 + -1x2 + x2 -5 + -3i + -3ix + -4x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -5 + -3i + -3ix + -4x + x2 = 0 The solution to this equation could not be determined.
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