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Simplifying [X + -1(5 + -3i)][x + -1(5 + 3i)] = 0 [X + (5 * -1 + -3i * -1)][x + -1(5 + 3i)] = 0 [X + (-5 + 3i)][x + -1(5 + 3i)] = 0 Reorder the terms: [-5 + X + 3i][x + -1(5 + 3i)] = 0 [-5 + X + 3i][x + (5 * -1 + 3i * -1)] = 0 [-5 + X + 3i][x + (-5 + -3i)] = 0 Reorder the terms: [-5 + X + 3i][-5 + -3i + x] = 0 Multiply [-5 + X + 3i] * [-5 + -3i + x] [-5[-5 + -3i + x] + X[-5 + -3i + x] + 3i * [-5 + -3i + x]] = 0 [[-5 * -5 + -3i * -5 + x * -5] + X[-5 + -3i + x] + 3i * [-5 + -3i + x]] = 0 [[25 + 15i + -5x] + X[-5 + -3i + x] + 3i * [-5 + -3i + x]] = 0 [25 + 15i + -5x + [-5 * X + -3i * X + x * X] + 3i * [-5 + -3i + x]] = 0 [25 + 15i + -5x + [-5X + -3iX + xX] + 3i * [-5 + -3i + x]] = 0 [25 + 15i + -5x + -5X + -3iX + xX + [-5 * 3i + -3i * 3i + x * 3i]] = 0 Reorder the terms: [25 + 15i + -5x + -5X + -3iX + xX + [-15i + 3ix + -9i2]] = 0 [25 + 15i + -5x + -5X + -3iX + xX + [-15i + 3ix + -9i2]] = 0 Reorder the terms: [25 + -5X + 15i + -15i + -3iX + 3ix + -9i2 + -5x + xX] = 0 Combine like terms: 15i + -15i = 0 [25 + -5X + 0 + -3iX + 3ix + -9i2 + -5x + xX] = 0 [25 + -5X + -3iX + 3ix + -9i2 + -5x + xX] = 0 Solving 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -5X + -3iX + 3ix + -9i2 + -5x + -25 + xX = 0 + -25 Reorder the terms: 25 + -25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + -25 -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + -25 Combine like terms: 0 + -25 = -25 -5X + -3iX + 3ix + -9i2 + -5x + xX = -25 Add '-3ix' to each side of the equation. -5X + -3iX + 3ix + -9i2 + -5x + -3ix + xX = -25 + -3ix Reorder the terms: -5X + -3iX + 3ix + -3ix + -9i2 + -5x + xX = -25 + -3ix Combine like terms: 3ix + -3ix = 0 -5X + -3iX + 0 + -9i2 + -5x + xX = -25 + -3ix -5X + -3iX + -9i2 + -5x + xX = -25 + -3ix Add '9i2' to each side of the equation. -5X + -3iX + -9i2 + -5x + 9i2 + xX = -25 + -3ix + 9i2 Reorder the terms: -5X + -3iX + -9i2 + 9i2 + -5x + xX = -25 + -3ix + 9i2 Combine like terms: -9i2 + 9i2 = 0 -5X + -3iX + 0 + -5x + xX = -25 + -3ix + 9i2 -5X + -3iX + -5x + xX = -25 + -3ix + 9i2 Add '5x' to each side of the equation. -5X + -3iX + -5x + 5x + xX = -25 + -3ix + 9i2 + 5x Combine like terms: -5x + 5x = 0 -5X + -3iX + 0 + xX = -25 + -3ix + 9i2 + 5x -5X + -3iX + xX = -25 + -3ix + 9i2 + 5x Reorder the terms: 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = -25 + -3ix + 9i2 + 5x + 25 + 3ix + -9i2 + -5x Reorder the terms: 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = -25 + 25 + -3ix + 3ix + 9i2 + -9i2 + 5x + -5x Combine like terms: -25 + 25 = 0 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + -3ix + 3ix + 9i2 + -9i2 + 5x + -5x 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = -3ix + 3ix + 9i2 + -9i2 + 5x + -5x Combine like terms: -3ix + 3ix = 0 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + 9i2 + -9i2 + 5x + -5x 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 9i2 + -9i2 + 5x + -5x Combine like terms: 9i2 + -9i2 = 0 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 + 5x + -5x 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 5x + -5x Combine like terms: 5x + -5x = 0 25 + -5X + -3iX + 3ix + -9i2 + -5x + xX = 0 The solution to this equation could not be determined.
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