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Simplifying 0 = [x + -1(4 + -1i)][x + -1(4 + i)] 0 = [x + (4 * -1 + -1i * -1)][x + -1(4 + i)] 0 = [x + (-4 + 1i)][x + -1(4 + i)] Reorder the terms: 0 = [-4 + 1i + x][x + -1(4 + i)] 0 = [-4 + 1i + x][x + (4 * -1 + i * -1)] 0 = [-4 + 1i + x][x + (-4 + -1i)] Reorder the terms: 0 = [-4 + 1i + x][-4 + -1i + x] Multiply [-4 + 1i + x] * [-4 + -1i + x] 0 = [-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]] Reorder the terms: 0 = [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]] Reorder the terms: 0 = [16 + 4i + -4x + -4i + 1ix + -1i2 + [-1ix + -4x + x2]] 0 = [16 + 4i + -4x + -4i + 1ix + -1i2 + [-1ix + -4x + x2]] Reorder the terms: 0 = [16 + 4i + -4i + 1ix + -1ix + -1i2 + -4x + -4x + x2] Combine like terms: 4i + -4i = 0 0 = [16 + 0 + 1ix + -1ix + -1i2 + -4x + -4x + x2] 0 = [16 + 1ix + -1ix + -1i2 + -4x + -4x + x2] Combine like terms: 1ix + -1ix = 0 0 = [16 + 0 + -1i2 + -4x + -4x + x2] 0 = [16 + -1i2 + -4x + -4x + x2] Combine like terms: -4x + -4x = -8x 0 = [16 + -1i2 + -8x + x2] Solving 0 = 16 + -1i2 + -8x + x2 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i2' to each side of the equation. 0 + i2 = 16 + -1i2 + -8x + i2 + x2 Remove the zero: i2 = 16 + -1i2 + -8x + i2 + x2 Reorder the terms: i2 = 16 + -1i2 + i2 + -8x + x2 Combine like terms: -1i2 + i2 = 0 i2 = 16 + 0 + -8x + x2 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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