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Simplifying [x + -1(3 + -1i)][x + -1(3 + i)] = 0 [x + (3 * -1 + -1i * -1)][x + -1(3 + i)] = 0 [x + (-3 + 1i)][x + -1(3 + i)] = 0 Reorder the terms: [-3 + 1i + x][x + -1(3 + i)] = 0 [-3 + 1i + x][x + (3 * -1 + i * -1)] = 0 [-3 + 1i + x][x + (-3 + -1i)] = 0 Reorder the terms: [-3 + 1i + x][-3 + -1i + x] = 0 Multiply [-3 + 1i + x] * [-3 + -1i + x] [-3[-3 + -1i + x] + 1i * [-3 + -1i + x] + x[-3 + -1i + x]] = 0 [[-3 * -3 + -1i * -3 + x * -3] + 1i * [-3 + -1i + x] + x[-3 + -1i + x]] = 0 [[9 + 3i + -3x] + 1i * [-3 + -1i + x] + x[-3 + -1i + x]] = 0 [9 + 3i + -3x + [-3 * 1i + -1i * 1i + x * 1i] + x[-3 + -1i + x]] = 0 Reorder the terms: [9 + 3i + -3x + [-3i + 1ix + -1i2] + x[-3 + -1i + x]] = 0 [9 + 3i + -3x + [-3i + 1ix + -1i2] + x[-3 + -1i + x]] = 0 [9 + 3i + -3x + -3i + 1ix + -1i2 + [-3 * x + -1i * x + x * x]] = 0 Reorder the terms: [9 + 3i + -3x + -3i + 1ix + -1i2 + [-1ix + -3x + x2]] = 0 [9 + 3i + -3x + -3i + 1ix + -1i2 + [-1ix + -3x + x2]] = 0 Reorder the terms: [9 + 3i + -3i + 1ix + -1ix + -1i2 + -3x + -3x + x2] = 0 Combine like terms: 3i + -3i = 0 [9 + 0 + 1ix + -1ix + -1i2 + -3x + -3x + x2] = 0 [9 + 1ix + -1ix + -1i2 + -3x + -3x + x2] = 0 Combine like terms: 1ix + -1ix = 0 [9 + 0 + -1i2 + -3x + -3x + x2] = 0 [9 + -1i2 + -3x + -3x + x2] = 0 Combine like terms: -3x + -3x = -6x [9 + -1i2 + -6x + x2] = 0 Solving 9 + -1i2 + -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 + -1i2 + -6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -1i2 + -6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i2 + -6x + x2 = 0 + -9 -1i2 + -6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -1i2 + -6x + x2 = -9 Add '6x' to each side of the equation. -1i2 + -6x + 6x + x2 = -9 + 6x Combine like terms: -6x + 6x = 0 -1i2 + 0 + x2 = -9 + 6x -1i2 + x2 = -9 + 6x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -9 + 6x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -9 + 6x + -1x2 -1i2 = -9 + 6x + -1x2 Divide each side by '-1'. i2 = 9 + -6x + x2 Simplifying i2 = 9 + -6x + x2 Reorder the terms: -9 + i2 + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -9 + i2 + 6x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -9 + i2 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -9 + i2 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -9 + i2 + 6x + -1x2 = 0 + x2 + -1x2 -9 + i2 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + i2 + 6x + -1x2 = 0 The solution to this equation could not be determined.
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