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Simplifying (x + -5)(x + -5)(x + 7i)(x + -7i) = 0 Reorder the terms: (-5 + x)(x + -5)(x + 7i)(x + -7i) = 0 Reorder the terms: (-5 + x)(-5 + x)(x + 7i)(x + -7i) = 0 Reorder the terms: (-5 + x)(-5 + x)(7i + x)(x + -7i) = 0 Reorder the terms: (-5 + x)(-5 + x)(7i + x)(-7i + x) = 0 Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x))(7i + x)(-7i + x) = 0 ((-5 * -5 + x * -5) + x(-5 + x))(7i + x)(-7i + x) = 0 ((25 + -5x) + x(-5 + x))(7i + x)(-7i + x) = 0 (25 + -5x + (-5 * x + x * x))(7i + x)(-7i + x) = 0 (25 + -5x + (-5x + x2))(7i + x)(-7i + x) = 0 Combine like terms: -5x + -5x = -10x (25 + -10x + x2)(7i + x)(-7i + x) = 0 Multiply (25 + -10x + x2) * (7i + x) (25(7i + x) + -10x * (7i + x) + x2(7i + x))(-7i + x) = 0 ((7i * 25 + x * 25) + -10x * (7i + x) + x2(7i + x))(-7i + x) = 0 ((175i + 25x) + -10x * (7i + x) + x2(7i + x))(-7i + x) = 0 (175i + 25x + (7i * -10x + x * -10x) + x2(7i + x))(-7i + x) = 0 (175i + 25x + (-70ix + -10x2) + x2(7i + x))(-7i + x) = 0 (175i + 25x + -70ix + -10x2 + (7i * x2 + x * x2))(-7i + x) = 0 (175i + 25x + -70ix + -10x2 + (7ix2 + x3))(-7i + x) = 0 Reorder the terms: (175i + -70ix + 7ix2 + 25x + -10x2 + x3)(-7i + x) = 0 (175i + -70ix + 7ix2 + 25x + -10x2 + x3)(-7i + x) = 0 Multiply (175i + -70ix + 7ix2 + 25x + -10x2 + x3) * (-7i + x) (175i * (-7i + x) + -70ix * (-7i + x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 ((-7i * 175i + x * 175i) + -70ix * (-7i + x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 Reorder the terms: ((175ix + -1225i2) + -70ix * (-7i + x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 ((175ix + -1225i2) + -70ix * (-7i + x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + (-7i * -70ix + x * -70ix) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 Reorder the terms: (175ix + -1225i2 + (-70ix2 + 490i2x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + (-70ix2 + 490i2x) + 7ix2 * (-7i + x) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + (-7i * 7ix2 + x * 7ix2) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 Reorder the terms: (175ix + -1225i2 + -70ix2 + 490i2x + (7ix3 + -49i2x2) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + (7ix3 + -49i2x2) + 25x * (-7i + x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + (-7i * 25x + x * 25x) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + (-175ix + 25x2) + -10x2 * (-7i + x) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + -175ix + 25x2 + (-7i * -10x2 + x * -10x2) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + -175ix + 25x2 + (70ix2 + -10x3) + x3(-7i + x)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + -175ix + 25x2 + 70ix2 + -10x3 + (-7i * x3 + x * x3)) = 0 (175ix + -1225i2 + -70ix2 + 490i2x + 7ix3 + -49i2x2 + -175ix + 25x2 + 70ix2 + -10x3 + (-7ix3 + x4)) = 0 Reorder the terms: (175ix + -175ix + -70ix2 + 70ix2 + 7ix3 + -7ix3 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: 175ix + -175ix = 0 (0 + -70ix2 + 70ix2 + 7ix3 + -7ix3 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 (-70ix2 + 70ix2 + 7ix3 + -7ix3 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: -70ix2 + 70ix2 = 0 (0 + 7ix3 + -7ix3 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 (7ix3 + -7ix3 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 Combine like terms: 7ix3 + -7ix3 = 0 (0 + -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 (-1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4) = 0 Solving -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-25x2' to each side of the equation. -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + -25x2 + x4 = 0 + -25x2 Reorder the terms: -1225i2 + 490i2x + -49i2x2 + 25x2 + -25x2 + -10x3 + x4 = 0 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -1225i2 + 490i2x + -49i2x2 + 0 + -10x3 + x4 = 0 + -25x2 -1225i2 + 490i2x + -49i2x2 + -10x3 + x4 = 0 + -25x2 Remove the zero: -1225i2 + 490i2x + -49i2x2 + -10x3 + x4 = -25x2 Add '10x3' to each side of the equation. -1225i2 + 490i2x + -49i2x2 + -10x3 + 10x3 + x4 = -25x2 + 10x3 Combine like terms: -10x3 + 10x3 = 0 -1225i2 + 490i2x + -49i2x2 + 0 + x4 = -25x2 + 10x3 -1225i2 + 490i2x + -49i2x2 + x4 = -25x2 + 10x3 Add '-1x4' to each side of the equation. -1225i2 + 490i2x + -49i2x2 + x4 + -1x4 = -25x2 + 10x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -1225i2 + 490i2x + -49i2x2 + 0 = -25x2 + 10x3 + -1x4 -1225i2 + 490i2x + -49i2x2 = -25x2 + 10x3 + -1x4 Reorder the terms: -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = -25x2 + 25x2 + 10x3 + -10x3 + -1x4 + x4 Combine like terms: -25x2 + 25x2 = 0 -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = 0 + 10x3 + -10x3 + -1x4 + x4 -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = 10x3 + -10x3 + -1x4 + x4 Combine like terms: 10x3 + -10x3 = 0 -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = 0 + -1x4 + x4 -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -1225i2 + 490i2x + -49i2x2 + 25x2 + -10x3 + x4 = 0 The solution to this equation could not be determined.
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