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Simplifying [x + -1(-4 + 4i)][x + -1(-4 + -4i)] = 0 [x + (-4 * -1 + 4i * -1)][x + -1(-4 + -4i)] = 0 [x + (4 + -4i)][x + -1(-4 + -4i)] = 0 Reorder the terms: [4 + -4i + x][x + -1(-4 + -4i)] = 0 [4 + -4i + x][x + (-4 * -1 + -4i * -1)] = 0 [4 + -4i + x][x + (4 + 4i)] = 0 Reorder the terms: [4 + -4i + x][4 + 4i + x] = 0 Multiply [4 + -4i + x] * [4 + 4i + x] [4[4 + 4i + x] + -4i * [4 + 4i + x] + x[4 + 4i + x]] = 0 [[4 * 4 + 4i * 4 + x * 4] + -4i * [4 + 4i + x] + x[4 + 4i + x]] = 0 [[16 + 16i + 4x] + -4i * [4 + 4i + x] + x[4 + 4i + x]] = 0 [16 + 16i + 4x + [4 * -4i + 4i * -4i + x * -4i] + x[4 + 4i + x]] = 0 Reorder the terms: [16 + 16i + 4x + [-16i + -4ix + -16i2] + x[4 + 4i + x]] = 0 [16 + 16i + 4x + [-16i + -4ix + -16i2] + x[4 + 4i + x]] = 0 [16 + 16i + 4x + -16i + -4ix + -16i2 + [4 * x + 4i * x + x * x]] = 0 Reorder the terms: [16 + 16i + 4x + -16i + -4ix + -16i2 + [4ix + 4x + x2]] = 0 [16 + 16i + 4x + -16i + -4ix + -16i2 + [4ix + 4x + x2]] = 0 Reorder the terms: [16 + 16i + -16i + -4ix + 4ix + -16i2 + 4x + 4x + x2] = 0 Combine like terms: 16i + -16i = 0 [16 + 0 + -4ix + 4ix + -16i2 + 4x + 4x + x2] = 0 [16 + -4ix + 4ix + -16i2 + 4x + 4x + x2] = 0 Combine like terms: -4ix + 4ix = 0 [16 + 0 + -16i2 + 4x + 4x + x2] = 0 [16 + -16i2 + 4x + 4x + x2] = 0 Combine like terms: 4x + 4x = 8x [16 + -16i2 + 8x + x2] = 0 Solving 16 + -16i2 + 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 + -16i2 + 8x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -16i2 + 8x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16i2 + 8x + x2 = 0 + -16 -16i2 + 8x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -16i2 + 8x + x2 = -16 Add '-8x' to each side of the equation. -16i2 + 8x + -8x + x2 = -16 + -8x Combine like terms: 8x + -8x = 0 -16i2 + 0 + x2 = -16 + -8x -16i2 + x2 = -16 + -8x Add '-1x2' to each side of the equation. -16i2 + x2 + -1x2 = -16 + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 -16i2 + 0 = -16 + -8x + -1x2 -16i2 = -16 + -8x + -1x2 Divide each side by '-16'. i2 = 1 + 0.5x + 0.0625x2 Simplifying i2 = 1 + 0.5x + 0.0625x2 Reorder the terms: -1 + i2 + -0.5x + -0.0625x2 = 1 + 0.5x + 0.0625x2 + -1 + -0.5x + -0.0625x2 Reorder the terms: -1 + i2 + -0.5x + -0.0625x2 = 1 + -1 + 0.5x + -0.5x + 0.0625x2 + -0.0625x2 Combine like terms: 1 + -1 = 0 -1 + i2 + -0.5x + -0.0625x2 = 0 + 0.5x + -0.5x + 0.0625x2 + -0.0625x2 -1 + i2 + -0.5x + -0.0625x2 = 0.5x + -0.5x + 0.0625x2 + -0.0625x2 Combine like terms: 0.5x + -0.5x = 0.0 -1 + i2 + -0.5x + -0.0625x2 = 0.0 + 0.0625x2 + -0.0625x2 -1 + i2 + -0.5x + -0.0625x2 = 0.0625x2 + -0.0625x2 Combine like terms: 0.0625x2 + -0.0625x2 = 0.0000 -1 + i2 + -0.5x + -0.0625x2 = 0.0000 The solution to this equation could not be determined.
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