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Simplifying (x + 20 + -30i)(x + 20 + 30i) = 0 Reorder the terms: (20 + -30i + x)(x + 20 + 30i) = 0 Reorder the terms: (20 + -30i + x)(20 + 30i + x) = 0 Multiply (20 + -30i + x) * (20 + 30i + x) (20(20 + 30i + x) + -30i * (20 + 30i + x) + x(20 + 30i + x)) = 0 ((20 * 20 + 30i * 20 + x * 20) + -30i * (20 + 30i + x) + x(20 + 30i + x)) = 0 ((400 + 600i + 20x) + -30i * (20 + 30i + x) + x(20 + 30i + x)) = 0 (400 + 600i + 20x + (20 * -30i + 30i * -30i + x * -30i) + x(20 + 30i + x)) = 0 Reorder the terms: (400 + 600i + 20x + (-600i + -30ix + -900i2) + x(20 + 30i + x)) = 0 (400 + 600i + 20x + (-600i + -30ix + -900i2) + x(20 + 30i + x)) = 0 (400 + 600i + 20x + -600i + -30ix + -900i2 + (20 * x + 30i * x + x * x)) = 0 Reorder the terms: (400 + 600i + 20x + -600i + -30ix + -900i2 + (30ix + 20x + x2)) = 0 (400 + 600i + 20x + -600i + -30ix + -900i2 + (30ix + 20x + x2)) = 0 Reorder the terms: (400 + 600i + -600i + -30ix + 30ix + -900i2 + 20x + 20x + x2) = 0 Combine like terms: 600i + -600i = 0 (400 + 0 + -30ix + 30ix + -900i2 + 20x + 20x + x2) = 0 (400 + -30ix + 30ix + -900i2 + 20x + 20x + x2) = 0 Combine like terms: -30ix + 30ix = 0 (400 + 0 + -900i2 + 20x + 20x + x2) = 0 (400 + -900i2 + 20x + 20x + x2) = 0 Combine like terms: 20x + 20x = 40x (400 + -900i2 + 40x + x2) = 0 Solving 400 + -900i2 + 40x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-400' to each side of the equation. 400 + -900i2 + 40x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -900i2 + 40x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -900i2 + 40x + x2 = 0 + -400 -900i2 + 40x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -900i2 + 40x + x2 = -400 Add '-40x' to each side of the equation. -900i2 + 40x + -40x + x2 = -400 + -40x Combine like terms: 40x + -40x = 0 -900i2 + 0 + x2 = -400 + -40x -900i2 + x2 = -400 + -40x Add '-1x2' to each side of the equation. -900i2 + x2 + -1x2 = -400 + -40x + -1x2 Combine like terms: x2 + -1x2 = 0 -900i2 + 0 = -400 + -40x + -1x2 -900i2 = -400 + -40x + -1x2 Divide each side by '-900'. i2 = 0.4444444444 + 0.04444444444x + 0.001111111111x2 Simplifying i2 = 0.4444444444 + 0.04444444444x + 0.001111111111x2 Reorder the terms: -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.4444444444 + 0.04444444444x + 0.001111111111x2 + -0.4444444444 + -0.04444444444x + -0.001111111111x2 Reorder the terms: -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.4444444444 + -0.4444444444 + 0.04444444444x + -0.04444444444x + 0.001111111111x2 + -0.001111111111x2 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.0000000000 + 0.04444444444x + -0.04444444444x + 0.001111111111x2 + -0.001111111111x2 -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.04444444444x + -0.04444444444x + 0.001111111111x2 + -0.001111111111x2 Combine like terms: 0.04444444444x + -0.04444444444x = 0.00000000000 -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.00000000000 + 0.001111111111x2 + -0.001111111111x2 -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.001111111111x2 + -0.001111111111x2 Combine like terms: 0.001111111111x2 + -0.001111111111x2 = 0.000000000000 -0.4444444444 + i2 + -0.04444444444x + -0.001111111111x2 = 0.000000000000 The solution to this equation could not be determined.
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