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Simplifying [x + -1(4 + i)][x + -1(4 + -1i)] = 0 [x + (4 * -1 + i * -1)][x + -1(4 + -1i)] = 0 [x + (-4 + -1i)][x + -1(4 + -1i)] = 0 Reorder the terms: [-4 + -1i + x][x + -1(4 + -1i)] = 0 [-4 + -1i + x][x + (4 * -1 + -1i * -1)] = 0 [-4 + -1i + x][x + (-4 + 1i)] = 0 Reorder the terms: [-4 + -1i + x][-4 + 1i + x] = 0 Multiply [-4 + -1i + x] * [-4 + 1i + x] [-4[-4 + 1i + x] + -1i * [-4 + 1i + x] + x[-4 + 1i + x]] = 0 [[-4 * -4 + 1i * -4 + x * -4] + -1i * [-4 + 1i + x] + x[-4 + 1i + x]] = 0 [[16 + -4i + -4x] + -1i * [-4 + 1i + x] + x[-4 + 1i + x]] = 0 [16 + -4i + -4x + [-4 * -1i + 1i * -1i + x * -1i] + x[-4 + 1i + x]] = 0 Reorder the terms: [16 + -4i + -4x + [4i + -1ix + -1i2] + x[-4 + 1i + x]] = 0 [16 + -4i + -4x + [4i + -1ix + -1i2] + x[-4 + 1i + x]] = 0 [16 + -4i + -4x + 4i + -1ix + -1i2 + [-4 * x + 1i * x + x * x]] = 0 Reorder the terms: [16 + -4i + -4x + 4i + -1ix + -1i2 + [1ix + -4x + x2]] = 0 [16 + -4i + -4x + 4i + -1ix + -1i2 + [1ix + -4x + x2]] = 0 Reorder the terms: [16 + -4i + 4i + -1ix + 1ix + -1i2 + -4x + -4x + x2] = 0 Combine like terms: -4i + 4i = 0 [16 + 0 + -1ix + 1ix + -1i2 + -4x + -4x + x2] = 0 [16 + -1ix + 1ix + -1i2 + -4x + -4x + x2] = 0 Combine like terms: -1ix + 1ix = 0 [16 + 0 + -1i2 + -4x + -4x + x2] = 0 [16 + -1i2 + -4x + -4x + x2] = 0 Combine like terms: -4x + -4x = -8x [16 + -1i2 + -8x + x2] = 0 Solving 16 + -1i2 + -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 + -1i2 + -8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -1i2 + -8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1i2 + -8x + x2 = 0 + -16 -1i2 + -8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -1i2 + -8x + x2 = -16 Add '8x' to each side of the equation. -1i2 + -8x + 8x + x2 = -16 + 8x Combine like terms: -8x + 8x = 0 -1i2 + 0 + x2 = -16 + 8x -1i2 + x2 = -16 + 8x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -16 + 8x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -16 + 8x + -1x2 -1i2 = -16 + 8x + -1x2 Divide each side by '-1'. i2 = 16 + -8x + x2 Simplifying i2 = 16 + -8x + x2 Reorder the terms: -16 + i2 + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2 Reorder the terms: -16 + i2 + 8x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 -16 + i2 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2 -16 + i2 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -16 + i2 + 8x + -1x2 = 0 + x2 + -1x2 -16 + i2 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + i2 + 8x + -1x2 = 0 The solution to this equation could not be determined.
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