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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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