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Simplifying [x + -1(4 + 3i)][x + -1(4 + -3i)] = 0 [x + (4 * -1 + 3i * -1)][x + -1(4 + -3i)] = 0 [x + (-4 + -3i)][x + -1(4 + -3i)] = 0 Reorder the terms: [-4 + -3i + x][x + -1(4 + -3i)] = 0 [-4 + -3i + x][x + (4 * -1 + -3i * -1)] = 0 [-4 + -3i + x][x + (-4 + 3i)] = 0 Reorder the terms: [-4 + -3i + x][-4 + 3i + x] = 0 Multiply [-4 + -3i + x] * [-4 + 3i + x] [-4[-4 + 3i + x] + -3i * [-4 + 3i + x] + x[-4 + 3i + x]] = 0 [[-4 * -4 + 3i * -4 + x * -4] + -3i * [-4 + 3i + x] + x[-4 + 3i + x]] = 0 [[16 + -12i + -4x] + -3i * [-4 + 3i + x] + x[-4 + 3i + x]] = 0 [16 + -12i + -4x + [-4 * -3i + 3i * -3i + x * -3i] + x[-4 + 3i + x]] = 0 Reorder the terms: [16 + -12i + -4x + [12i + -3ix + -9i2] + x[-4 + 3i + x]] = 0 [16 + -12i + -4x + [12i + -3ix + -9i2] + x[-4 + 3i + x]] = 0 [16 + -12i + -4x + 12i + -3ix + -9i2 + [-4 * x + 3i * x + x * x]] = 0 Reorder the terms: [16 + -12i + -4x + 12i + -3ix + -9i2 + [3ix + -4x + x2]] = 0 [16 + -12i + -4x + 12i + -3ix + -9i2 + [3ix + -4x + x2]] = 0 Reorder the terms: [16 + -12i + 12i + -3ix + 3ix + -9i2 + -4x + -4x + x2] = 0 Combine like terms: -12i + 12i = 0 [16 + 0 + -3ix + 3ix + -9i2 + -4x + -4x + x2] = 0 [16 + -3ix + 3ix + -9i2 + -4x + -4x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [16 + 0 + -9i2 + -4x + -4x + x2] = 0 [16 + -9i2 + -4x + -4x + x2] = 0 Combine like terms: -4x + -4x = -8x [16 + -9i2 + -8x + x2] = 0 Solving 16 + -9i2 + -8x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -9i2 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -9i2 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -9i2 + -8x + x2 = 0 + -16 -9i2 + -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -9i2 + -8x + x2 = -16 Add '8x' to each side of the equation. -9i2 + -8x + 8x + x2 = -16 + 8x Combine like terms: -8x + 8x = 0 -9i2 + 0 + x2 = -16 + 8x -9i2 + x2 = -16 + 8x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -16 + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -16 + 8x + -1x2 -9i2 = -16 + 8x + -1x2 Divide each side by '-9'. i2 = 1.777777778 + -0.8888888889x + 0.1111111111x2 Simplifying i2 = 1.777777778 + -0.8888888889x + 0.1111111111x2 Reorder the terms: -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 1.777777778 + -0.8888888889x + 0.1111111111x2 + -1.777777778 + 0.8888888889x + -0.1111111111x2 Reorder the terms: -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 1.777777778 + -1.777777778 + -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 0.000000000 + -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -0.8888888889x + 0.8888888889x = 0.0000000000 -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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