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Simplifying (x + -1(-5 + 3i))(x + 5 + 3i) = 0 (x + (-5 * -1 + 3i * -1))(x + 5 + 3i) = 0 (x + (5 + -3i))(x + 5 + 3i) = 0 Reorder the terms: (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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