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Simplifying (x + 5 + -1i)(x + 5 + i) = 0 Reorder the terms: (5 + -1i + x)(x + 5 + i) = 0 Reorder the terms: (5 + -1i + x)(5 + i + x) = 0 Multiply (5 + -1i + x) * (5 + i + x) (5(5 + i + x) + -1i * (5 + i + x) + x(5 + i + x)) = 0 ((5 * 5 + i * 5 + x * 5) + -1i * (5 + i + x) + x(5 + i + x)) = 0 ((25 + 5i + 5x) + -1i * (5 + i + x) + x(5 + i + x)) = 0 (25 + 5i + 5x + (5 * -1i + i * -1i + x * -1i) + x(5 + i + x)) = 0 Reorder the terms: (25 + 5i + 5x + (-5i + -1ix + -1i2) + x(5 + i + x)) = 0 (25 + 5i + 5x + (-5i + -1ix + -1i2) + x(5 + i + x)) = 0 (25 + 5i + 5x + -5i + -1ix + -1i2 + (5 * x + i * x + x * x)) = 0 Reorder the terms: (25 + 5i + 5x + -5i + -1ix + -1i2 + (ix + 5x + x2)) = 0 (25 + 5i + 5x + -5i + -1ix + -1i2 + (ix + 5x + x2)) = 0 Reorder the terms: (25 + 5i + -5i + -1ix + ix + -1i2 + 5x + 5x + x2) = 0 Combine like terms: 5i + -5i = 0 (25 + 0 + -1ix + ix + -1i2 + 5x + 5x + x2) = 0 (25 + -1ix + ix + -1i2 + 5x + 5x + x2) = 0 Combine like terms: -1ix + ix = 0 (25 + 0 + -1i2 + 5x + 5x + x2) = 0 (25 + -1i2 + 5x + 5x + x2) = 0 Combine like terms: 5x + 5x = 10x (25 + -1i2 + 10x + x2) = 0 Solving 25 + -1i2 + 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 + -1i2 + 10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -1i2 + 10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1i2 + 10x + x2 = 0 + -25 -1i2 + 10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -1i2 + 10x + x2 = -25 Add '-10x' to each side of the equation. -1i2 + 10x + -10x + x2 = -25 + -10x Combine like terms: 10x + -10x = 0 -1i2 + 0 + x2 = -25 + -10x -1i2 + x2 = -25 + -10x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -25 + -10x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -25 + -10x + -1x2 -1i2 = -25 + -10x + -1x2 Divide each side by '-1'. i2 = 25 + 10x + x2 Simplifying i2 = 25 + 10x + x2 Reorder the terms: -25 + i2 + -10x + -1x2 = 25 + 10x + x2 + -25 + -10x + -1x2 Reorder the terms: -25 + i2 + -10x + -1x2 = 25 + -25 + 10x + -10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 -25 + i2 + -10x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -25 + i2 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -25 + i2 + -10x + -1x2 = 0 + x2 + -1x2 -25 + i2 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -25 + i2 + -10x + -1x2 = 0 The solution to this equation could not be determined.
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