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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 + -3i + x][x + -1(5 + -3i)] = 0 [-5 + -3i + x][x + (5 * -1 + -3i * -1)] = 0 [-5 + -3i + x][x + (-5 + 3i)] = 0 Reorder the terms: [-5 + -3i + x][-5 + 3i + x] = 0 Multiply [-5 + -3i + x] * [-5 + 3i + x] [-5[-5 + 3i + x] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] = 0 [[-5 * -5 + 3i * -5 + x * -5] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] = 0 [[25 + -15i + -5x] + -3i * [-5 + 3i + x] + x[-5 + 3i + x]] = 0 [25 + -15i + -5x + [-5 * -3i + 3i * -3i + x * -3i] + x[-5 + 3i + x]] = 0 Reorder the terms: [25 + -15i + -5x + [15i + -3ix + -9i2] + x[-5 + 3i + x]] = 0 [25 + -15i + -5x + [15i + -3ix + -9i2] + x[-5 + 3i + x]] = 0 [25 + -15i + -5x + 15i + -3ix + -9i2 + [-5 * x + 3i * x + x * x]] = 0 Reorder the terms: [25 + -15i + -5x + 15i + -3ix + -9i2 + [3ix + -5x + x2]] = 0 [25 + -15i + -5x + 15i + -3ix + -9i2 + [3ix + -5x + x2]] = 0 Reorder the terms: [25 + -15i + 15i + -3ix + 3ix + -9i2 + -5x + -5x + x2] = 0 Combine like terms: -15i + 15i = 0 [25 + 0 + -3ix + 3ix + -9i2 + -5x + -5x + x2] = 0 [25 + -3ix + 3ix + -9i2 + -5x + -5x + x2] = 0 Combine like terms: -3ix + 3ix = 0 [25 + 0 + -9i2 + -5x + -5x + x2] = 0 [25 + -9i2 + -5x + -5x + x2] = 0 Combine like terms: -5x + -5x = -10x [25 + -9i2 + -10x + x2] = 0 Solving 25 + -9i2 + -10x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -9i2 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -9i2 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -9i2 + -10x + x2 = 0 + -25 -9i2 + -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -9i2 + -10x + x2 = -25 Add '10x' to each side of the equation. -9i2 + -10x + 10x + x2 = -25 + 10x Combine like terms: -10x + 10x = 0 -9i2 + 0 + x2 = -25 + 10x -9i2 + x2 = -25 + 10x Add '-1x2' to each side of the equation. -9i2 + x2 + -1x2 = -25 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 -9i2 + 0 = -25 + 10x + -1x2 -9i2 = -25 + 10x + -1x2 Divide each side by '-9'. i2 = 2.777777778 + -1.111111111x + 0.1111111111x2 Simplifying i2 = 2.777777778 + -1.111111111x + 0.1111111111x2 Reorder the terms: -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 2.777777778 + -1.111111111x + 0.1111111111x2 + -2.777777778 + 1.111111111x + -0.1111111111x2 Reorder the terms: -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 2.777777778 + -2.777777778 + -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: 2.777777778 + -2.777777778 = 0.000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.000000000 + -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = -1.111111111x + 1.111111111x + 0.1111111111x2 + -0.1111111111x2 Combine like terms: -1.111111111x + 1.111111111x = 0.000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2 Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000 -2.777777778 + i2 + 1.111111111x + -0.1111111111x2 = 0.0000000000 The solution to this equation could not be determined.
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