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Simplifying [x + -1(-3 + 3i)][x + -1(-3 + -3i)] = 0 [x + (-3 * -1 + 3i * -1)][x + -1(-3 + -3i)] = 0 [x + (3 + -3i)][x + -1(-3 + -3i)] = 0 Reorder the terms: [3 + -3i + x][x + -1(-3 + -3i)] = 0 [3 + -3i + x][x + (-3 * -1 + -3i * -1)] = 0 [3 + -3i + x][x + (3 + 3i)] = 0 Reorder the terms: [3 + -3i + x][3 + 3i + x] = 0 Multiply [3 + -3i + x] * [3 + 3i + x] [3[3 + 3i + x] + -3i * [3 + 3i + x] + x[3 + 3i + x]] = 0 [[3 * 3 + 3i * 3 + x * 3] + -3i * [3 + 3i + x] + x[3 + 3i + x]] = 0 [[9 + 9i + 3x] + -3i * [3 + 3i + x] + x[3 + 3i + x]] = 0 [9 + 9i + 3x + [3 * -3i + 3i * -3i + x * -3i] + x[3 + 3i + x]] = 0 Reorder the terms: [9 + 9i + 3x + [-9i + -3ix + -9i2] + x[3 + 3i + x]] = 0 [9 + 9i + 3x + [-9i + -3ix + -9i2] + x[3 + 3i + x]] = 0 [9 + 9i + 3x + -9i + -3ix + -9i2 + [3 * x + 3i * x + x * x]] = 0 Reorder the terms: [9 + 9i + 3x + -9i + -3ix + -9i2 + [3ix + 3x + x2]] = 0 [9 + 9i + 3x + -9i + -3ix + -9i2 + [3ix + 3x + x2]] = 0 Reorder the terms: [9 + 9i + -9i + -3ix + 3ix + -9i2 + 3x + 3x + x2] = 0 Combine like terms: 9i + -9i = 0 [9 + 0 + -3ix + 3ix + -9i2 + 3x + 3x + x2] = 0 [9 + -3ix + 3ix + -9i2 + 3x + 3x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [9 + 0 + -9i2 + 3x + 3x + x2] = 0 [9 + -9i2 + 3x + 3x + x2] = 0 Combine like terms: 3x + 3x = 6x [9 + -9i2 + 6x + x2] = 0 Solving 9 + -9i2 + 6x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9i2 + 6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -9i2 + 6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9i2 + 6x + x2 = 0 + -9 -9i2 + 6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9i2 + 6x + x2 = -9 Add '-6x' to each side of the equation. -9i2 + 6x + -6x + x2 = -9 + -6x Combine like terms: 6x + -6x = 0 -9i2 + 0 + x2 = -9 + -6x -9i2 + x2 = -9 + -6x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -9 + -6x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -9 + -6x + -1x2 -9i2 = -9 + -6x + -1x2 Divide each side by '-9'. i2 = 1 + 0.6666666667x + 0.1111111111x2 Simplifying i2 = 1 + 0.6666666667x + 0.1111111111x2 Reorder the terms: -1 + i2 + -0.6666666667x + -0.1111111111x2 = 1 + 0.6666666667x + 0.1111111111x2 + -1 + -0.6666666667x + -0.1111111111x2 Reorder the terms: -1 + i2 + -0.6666666667x + -0.1111111111x2 = 1 + -1 + 0.6666666667x + -0.6666666667x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 1 + -1 = 0 -1 + i2 + -0.6666666667x + -0.1111111111x2 = 0 + 0.6666666667x + -0.6666666667x + 0.1111111111x2 + -0.1111111111x2 -1 + i2 + -0.6666666667x + -0.1111111111x2 = 0.6666666667x + -0.6666666667x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.6666666667x + -0.6666666667x = 0.0000000000 -1 + i2 + -0.6666666667x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -1 + i2 + -0.6666666667x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -1 + i2 + -0.6666666667x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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