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Simplifying [x + -1(1 + -3i)][x + -1(1 + 3i)] = 0 [x + (1 * -1 + -3i * -1)][x + -1(1 + 3i)] = 0 [x + (-1 + 3i)][x + -1(1 + 3i)] = 0 Reorder the terms: [-1 + 3i + x][x + -1(1 + 3i)] = 0 [-1 + 3i + x][x + (1 * -1 + 3i * -1)] = 0 [-1 + 3i + x][x + (-1 + -3i)] = 0 Reorder the terms: [-1 + 3i + x][-1 + -3i + x] = 0 Multiply [-1 + 3i + x] * [-1 + -3i + x] [-1[-1 + -3i + x] + 3i * [-1 + -3i + x] + x[-1 + -3i + x]] = 0 [[-1 * -1 + -3i * -1 + x * -1] + 3i * [-1 + -3i + x] + x[-1 + -3i + x]] = 0 [[1 + 3i + -1x] + 3i * [-1 + -3i + x] + x[-1 + -3i + x]] = 0 [1 + 3i + -1x + [-1 * 3i + -3i * 3i + x * 3i] + x[-1 + -3i + x]] = 0 Reorder the terms: [1 + 3i + -1x + [-3i + 3ix + -9i2] + x[-1 + -3i + x]] = 0 [1 + 3i + -1x + [-3i + 3ix + -9i2] + x[-1 + -3i + x]] = 0 [1 + 3i + -1x + -3i + 3ix + -9i2 + [-1 * x + -3i * x + x * x]] = 0 Reorder the terms: [1 + 3i + -1x + -3i + 3ix + -9i2 + [-3ix + -1x + x2]] = 0 [1 + 3i + -1x + -3i + 3ix + -9i2 + [-3ix + -1x + x2]] = 0 Reorder the terms: [1 + 3i + -3i + 3ix + -3ix + -9i2 + -1x + -1x + x2] = 0 Combine like terms: 3i + -3i = 0 [1 + 0 + 3ix + -3ix + -9i2 + -1x + -1x + x2] = 0 [1 + 3ix + -3ix + -9i2 + -1x + -1x + x2] = 0 Combine like terms: 3ix + -3ix = 0 [1 + 0 + -9i2 + -1x + -1x + x2] = 0 [1 + -9i2 + -1x + -1x + x2] = 0 Combine like terms: -1x + -1x = -2x [1 + -9i2 + -2x + x2] = 0 Solving 1 + -9i2 + -2x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -9i2 + -2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -9i2 + -2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9i2 + -2x + x2 = 0 + -1 -9i2 + -2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9i2 + -2x + x2 = -1 Add '2x' to each side of the equation. -9i2 + -2x + 2x + x2 = -1 + 2x Combine like terms: -2x + 2x = 0 -9i2 + 0 + x2 = -1 + 2x -9i2 + x2 = -1 + 2x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -1 + 2x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -1 + 2x + -1x2 -9i2 = -1 + 2x + -1x2 Divide each side by '-9'. i2 = 0.1111111111 + -0.2222222222x + 0.1111111111x2 Simplifying i2 = 0.1111111111 + -0.2222222222x + 0.1111111111x2 Reorder the terms: -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.1111111111 + -0.2222222222x + 0.1111111111x2 + -0.1111111111 + 0.2222222222x + -0.1111111111x2 Reorder the terms: -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.1111111111 + -0.1111111111 + -0.2222222222x + 0.2222222222x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.0000000000 + -0.2222222222x + 0.2222222222x + 0.1111111111x2 + -0.1111111111x2 -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = -0.2222222222x + 0.2222222222x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -0.2222222222x + 0.2222222222x = 0.0000000000 -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -0.1111111111 + i2 + 0.2222222222x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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