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Simplifying (x + (3 + 5i))(x + (3 + -5i)) = 0 Remove parenthesis around (3 + 5i) (x + 3 + 5i)(x + (3 + -5i)) = 0 Reorder the terms: (3 + 5i + x)(x + (3 + -5i)) = 0 Remove parenthesis around (3 + -5i) (3 + 5i + x)(x + 3 + -5i) = 0 Reorder the terms: (3 + 5i + x)(3 + -5i + x) = 0 Multiply (3 + 5i + x) * (3 + -5i + x) (3(3 + -5i + x) + 5i * (3 + -5i + x) + x(3 + -5i + x)) = 0 ((3 * 3 + -5i * 3 + x * 3) + 5i * (3 + -5i + x) + x(3 + -5i + x)) = 0 ((9 + -15i + 3x) + 5i * (3 + -5i + x) + x(3 + -5i + x)) = 0 (9 + -15i + 3x + (3 * 5i + -5i * 5i + x * 5i) + x(3 + -5i + x)) = 0 Reorder the terms: (9 + -15i + 3x + (15i + 5ix + -25i2) + x(3 + -5i + x)) = 0 (9 + -15i + 3x + (15i + 5ix + -25i2) + x(3 + -5i + x)) = 0 (9 + -15i + 3x + 15i + 5ix + -25i2 + (3 * x + -5i * x + x * x)) = 0 Reorder the terms: (9 + -15i + 3x + 15i + 5ix + -25i2 + (-5ix + 3x + x2)) = 0 (9 + -15i + 3x + 15i + 5ix + -25i2 + (-5ix + 3x + x2)) = 0 Reorder the terms: (9 + -15i + 15i + 5ix + -5ix + -25i2 + 3x + 3x + x2) = 0 Combine like terms: -15i + 15i = 0 (9 + 0 + 5ix + -5ix + -25i2 + 3x + 3x + x2) = 0 (9 + 5ix + -5ix + -25i2 + 3x + 3x + x2) = 0 Combine like terms: 5ix + -5ix = 0 (9 + 0 + -25i2 + 3x + 3x + x2) = 0 (9 + -25i2 + 3x + 3x + x2) = 0 Combine like terms: 3x + 3x = 6x (9 + -25i2 + 6x + x2) = 0 Solving 9 + -25i2 + 6x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -25i2 + 6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -25i2 + 6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -25i2 + 6x + x2 = 0 + -9 -25i2 + 6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -25i2 + 6x + x2 = -9 Add '-6x' to each side of the equation. -25i2 + 6x + -6x + x2 = -9 + -6x Combine like terms: 6x + -6x = 0 -25i2 + 0 + x2 = -9 + -6x -25i2 + x2 = -9 + -6x Add '-1x2' to each side of the equation. -25i2 + x2 + -1x2 = -9 + -6x + -1x2 Combine like terms: x2 + -1x2 = 0 -25i2 + 0 = -9 + -6x + -1x2 -25i2 = -9 + -6x + -1x2 Divide each side by '-25'. i2 = 0.36 + 0.24x + 0.04x2 Simplifying i2 = 0.36 + 0.24x + 0.04x2 Reorder the terms: -0.36 + i2 + -0.24x + -0.04x2 = 0.36 + 0.24x + 0.04x2 + -0.36 + -0.24x + -0.04x2 Reorder the terms: -0.36 + i2 + -0.24x + -0.04x2 = 0.36 + -0.36 + 0.24x + -0.24x + 0.04x2 + -0.04x2 Combine like terms: 0.36 + -0.36 = 0.00 -0.36 + i2 + -0.24x + -0.04x2 = 0.00 + 0.24x + -0.24x + 0.04x2 + -0.04x2 -0.36 + i2 + -0.24x + -0.04x2 = 0.24x + -0.24x + 0.04x2 + -0.04x2 Combine like terms: 0.24x + -0.24x = 0.00 -0.36 + i2 + -0.24x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 -0.36 + i2 + -0.24x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 -0.36 + i2 + -0.24x + -0.04x2 = 0.00 The solution to this equation could not be determined.
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