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Simplifying [x + -1(-2 + 3i)][x + -1(-2 + -3i)] = 0 [x + (-2 * -1 + 3i * -1)][x + -1(-2 + -3i)] = 0 [x + (2 + -3i)][x + -1(-2 + -3i)] = 0 Reorder the terms: [2 + -3i + x][x + -1(-2 + -3i)] = 0 [2 + -3i + x][x + (-2 * -1 + -3i * -1)] = 0 [2 + -3i + x][x + (2 + 3i)] = 0 Reorder the terms: [2 + -3i + x][2 + 3i + x] = 0 Multiply [2 + -3i + x] * [2 + 3i + x] [2[2 + 3i + x] + -3i * [2 + 3i + x] + x[2 + 3i + x]] = 0 [[2 * 2 + 3i * 2 + x * 2] + -3i * [2 + 3i + x] + x[2 + 3i + x]] = 0 [[4 + 6i + 2x] + -3i * [2 + 3i + x] + x[2 + 3i + x]] = 0 [4 + 6i + 2x + [2 * -3i + 3i * -3i + x * -3i] + x[2 + 3i + x]] = 0 Reorder the terms: [4 + 6i + 2x + [-6i + -3ix + -9i2] + x[2 + 3i + x]] = 0 [4 + 6i + 2x + [-6i + -3ix + -9i2] + x[2 + 3i + x]] = 0 [4 + 6i + 2x + -6i + -3ix + -9i2 + [2 * x + 3i * x + x * x]] = 0 Reorder the terms: [4 + 6i + 2x + -6i + -3ix + -9i2 + [3ix + 2x + x2]] = 0 [4 + 6i + 2x + -6i + -3ix + -9i2 + [3ix + 2x + x2]] = 0 Reorder the terms: [4 + 6i + -6i + -3ix + 3ix + -9i2 + 2x + 2x + x2] = 0 Combine like terms: 6i + -6i = 0 [4 + 0 + -3ix + 3ix + -9i2 + 2x + 2x + x2] = 0 [4 + -3ix + 3ix + -9i2 + 2x + 2x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [4 + 0 + -9i2 + 2x + 2x + x2] = 0 [4 + -9i2 + 2x + 2x + x2] = 0 Combine like terms: 2x + 2x = 4x [4 + -9i2 + 4x + x2] = 0 Solving 4 + -9i2 + 4x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -9i2 + 4x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -9i2 + 4x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9i2 + 4x + x2 = 0 + -4 -9i2 + 4x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9i2 + 4x + x2 = -4 Add '-4x' to each side of the equation. -9i2 + 4x + -4x + x2 = -4 + -4x Combine like terms: 4x + -4x = 0 -9i2 + 0 + x2 = -4 + -4x -9i2 + x2 = -4 + -4x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -4 + -4x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -4 + -4x + -1x2 -9i2 = -4 + -4x + -1x2 Divide each side by '-9'. i2 = 0.4444444444 + 0.4444444444x + 0.1111111111x2 Simplifying i2 = 0.4444444444 + 0.4444444444x + 0.1111111111x2 Reorder the terms: -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.4444444444 + 0.4444444444x + 0.1111111111x2 + -0.4444444444 + -0.4444444444x + -0.1111111111x2 Reorder the terms: -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.4444444444 + -0.4444444444 + 0.4444444444x + -0.4444444444x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.0000000000 + 0.4444444444x + -0.4444444444x + 0.1111111111x2 + -0.1111111111x2 -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.4444444444x + -0.4444444444x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.4444444444x + -0.4444444444x = 0.0000000000 -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -0.4444444444 + i2 + -0.4444444444x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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