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Simplifying [x + -1(6 + 3i)][x + -1(6 + -3i)] = 0 [x + (6 * -1 + 3i * -1)][x + -1(6 + -3i)] = 0 [x + (-6 + -3i)][x + -1(6 + -3i)] = 0 Reorder the terms: [-6 + -3i + x][x + -1(6 + -3i)] = 0 [-6 + -3i + x][x + (6 * -1 + -3i * -1)] = 0 [-6 + -3i + x][x + (-6 + 3i)] = 0 Reorder the terms: [-6 + -3i + x][-6 + 3i + x] = 0 Multiply [-6 + -3i + x] * [-6 + 3i + x] [-6[-6 + 3i + x] + -3i * [-6 + 3i + x] + x[-6 + 3i + x]] = 0 [[-6 * -6 + 3i * -6 + x * -6] + -3i * [-6 + 3i + x] + x[-6 + 3i + x]] = 0 [[36 + -18i + -6x] + -3i * [-6 + 3i + x] + x[-6 + 3i + x]] = 0 [36 + -18i + -6x + [-6 * -3i + 3i * -3i + x * -3i] + x[-6 + 3i + x]] = 0 Reorder the terms: [36 + -18i + -6x + [18i + -3ix + -9i2] + x[-6 + 3i + x]] = 0 [36 + -18i + -6x + [18i + -3ix + -9i2] + x[-6 + 3i + x]] = 0 [36 + -18i + -6x + 18i + -3ix + -9i2 + [-6 * x + 3i * x + x * x]] = 0 Reorder the terms: [36 + -18i + -6x + 18i + -3ix + -9i2 + [3ix + -6x + x2]] = 0 [36 + -18i + -6x + 18i + -3ix + -9i2 + [3ix + -6x + x2]] = 0 Reorder the terms: [36 + -18i + 18i + -3ix + 3ix + -9i2 + -6x + -6x + x2] = 0 Combine like terms: -18i + 18i = 0 [36 + 0 + -3ix + 3ix + -9i2 + -6x + -6x + x2] = 0 [36 + -3ix + 3ix + -9i2 + -6x + -6x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [36 + 0 + -9i2 + -6x + -6x + x2] = 0 [36 + -9i2 + -6x + -6x + x2] = 0 Combine like terms: -6x + -6x = -12x [36 + -9i2 + -12x + x2] = 0 Solving 36 + -9i2 + -12x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -9i2 + -12x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -9i2 + -12x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -9i2 + -12x + x2 = 0 + -36 -9i2 + -12x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -9i2 + -12x + x2 = -36 Add '12x' to each side of the equation. -9i2 + -12x + 12x + x2 = -36 + 12x Combine like terms: -12x + 12x = 0 -9i2 + 0 + x2 = -36 + 12x -9i2 + x2 = -36 + 12x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -36 + 12x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -36 + 12x + -1x2 -9i2 = -36 + 12x + -1x2 Divide each side by '-9'. i2 = 4 + -1.333333333x + 0.1111111111x2 Simplifying i2 = 4 + -1.333333333x + 0.1111111111x2 Reorder the terms: -4 + i2 + 1.333333333x + -0.1111111111x2 = 4 + -1.333333333x + 0.1111111111x2 + -4 + 1.333333333x + -0.1111111111x2 Reorder the terms: -4 + i2 + 1.333333333x + -0.1111111111x2 = 4 + -4 + -1.333333333x + 1.333333333x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 4 + -4 = 0 -4 + i2 + 1.333333333x + -0.1111111111x2 = 0 + -1.333333333x + 1.333333333x + 0.1111111111x2 + -0.1111111111x2 -4 + i2 + 1.333333333x + -0.1111111111x2 = -1.333333333x + 1.333333333x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -1.333333333x + 1.333333333x = 0.000000000 -4 + i2 + 1.333333333x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2 -4 + i2 + 1.333333333x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -4 + i2 + 1.333333333x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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