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Simplifying [x + -1(8 + 3i)][x + -1(8 + -3i)] = 0 [x + (8 * -1 + 3i * -1)][x + -1(8 + -3i)] = 0 [x + (-8 + -3i)][x + -1(8 + -3i)] = 0 Reorder the terms: [-8 + -3i + x][x + -1(8 + -3i)] = 0 [-8 + -3i + x][x + (8 * -1 + -3i * -1)] = 0 [-8 + -3i + x][x + (-8 + 3i)] = 0 Reorder the terms: [-8 + -3i + x][-8 + 3i + x] = 0 Multiply [-8 + -3i + x] * [-8 + 3i + x] [-8[-8 + 3i + x] + -3i * [-8 + 3i + x] + x[-8 + 3i + x]] = 0 [[-8 * -8 + 3i * -8 + x * -8] + -3i * [-8 + 3i + x] + x[-8 + 3i + x]] = 0 [[64 + -24i + -8x] + -3i * [-8 + 3i + x] + x[-8 + 3i + x]] = 0 [64 + -24i + -8x + [-8 * -3i + 3i * -3i + x * -3i] + x[-8 + 3i + x]] = 0 Reorder the terms: [64 + -24i + -8x + [24i + -3ix + -9i2] + x[-8 + 3i + x]] = 0 [64 + -24i + -8x + [24i + -3ix + -9i2] + x[-8 + 3i + x]] = 0 [64 + -24i + -8x + 24i + -3ix + -9i2 + [-8 * x + 3i * x + x * x]] = 0 Reorder the terms: [64 + -24i + -8x + 24i + -3ix + -9i2 + [3ix + -8x + x2]] = 0 [64 + -24i + -8x + 24i + -3ix + -9i2 + [3ix + -8x + x2]] = 0 Reorder the terms: [64 + -24i + 24i + -3ix + 3ix + -9i2 + -8x + -8x + x2] = 0 Combine like terms: -24i + 24i = 0 [64 + 0 + -3ix + 3ix + -9i2 + -8x + -8x + x2] = 0 [64 + -3ix + 3ix + -9i2 + -8x + -8x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [64 + 0 + -9i2 + -8x + -8x + x2] = 0 [64 + -9i2 + -8x + -8x + x2] = 0 Combine like terms: -8x + -8x = -16x [64 + -9i2 + -16x + x2] = 0 Solving 64 + -9i2 + -16x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -9i2 + -16x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -9i2 + -16x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -9i2 + -16x + x2 = 0 + -64 -9i2 + -16x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -9i2 + -16x + x2 = -64 Add '16x' to each side of the equation. -9i2 + -16x + 16x + x2 = -64 + 16x Combine like terms: -16x + 16x = 0 -9i2 + 0 + x2 = -64 + 16x -9i2 + x2 = -64 + 16x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -64 + 16x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -64 + 16x + -1x2 -9i2 = -64 + 16x + -1x2 Divide each side by '-9'. i2 = 7.111111111 + -1.777777778x + 0.1111111111x2 Simplifying i2 = 7.111111111 + -1.777777778x + 0.1111111111x2 Reorder the terms: -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 7.111111111 + -1.777777778x + 0.1111111111x2 + -7.111111111 + 1.777777778x + -0.1111111111x2 Reorder the terms: -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 7.111111111 + -7.111111111 + -1.777777778x + 1.777777778x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 0.000000000 + -1.777777778x + 1.777777778x + 0.1111111111x2 + -0.1111111111x2 -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = -1.777777778x + 1.777777778x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -1.777777778x + 1.777777778x = 0.000000000 -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2 -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -7.111111111 + i2 + 1.777777778x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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