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Simplifying y = (x + -1(2 + -5i))(x + -1(2 + 5i)) y = (x + (2 * -1 + -5i * -1))(x + -1(2 + 5i)) y = (x + (-2 + 5i))(x + -1(2 + 5i)) Reorder the terms: y = (-2 + 5i + x)(x + -1(2 + 5i)) y = (-2 + 5i + x)(x + (2 * -1 + 5i * -1)) y = (-2 + 5i + x)(x + (-2 + -5i)) Reorder the terms: y = (-2 + 5i + x)(-2 + -5i + x) Multiply (-2 + 5i + x) * (-2 + -5i + x) y = (-2(-2 + -5i + x) + 5i * (-2 + -5i + x) + x(-2 + -5i + x)) y = ((-2 * -2 + -5i * -2 + x * -2) + 5i * (-2 + -5i + x) + x(-2 + -5i + x)) y = ((4 + 10i + -2x) + 5i * (-2 + -5i + x) + x(-2 + -5i + x)) y = (4 + 10i + -2x + (-2 * 5i + -5i * 5i + x * 5i) + x(-2 + -5i + x)) Reorder the terms: y = (4 + 10i + -2x + (-10i + 5ix + -25i2) + x(-2 + -5i + x)) y = (4 + 10i + -2x + (-10i + 5ix + -25i2) + x(-2 + -5i + x)) y = (4 + 10i + -2x + -10i + 5ix + -25i2 + (-2 * x + -5i * x + x * x)) Reorder the terms: y = (4 + 10i + -2x + -10i + 5ix + -25i2 + (-5ix + -2x + x2)) y = (4 + 10i + -2x + -10i + 5ix + -25i2 + (-5ix + -2x + x2)) Reorder the terms: y = (4 + 10i + -10i + 5ix + -5ix + -25i2 + -2x + -2x + x2) Combine like terms: 10i + -10i = 0 y = (4 + 0 + 5ix + -5ix + -25i2 + -2x + -2x + x2) y = (4 + 5ix + -5ix + -25i2 + -2x + -2x + x2) Combine like terms: 5ix + -5ix = 0 y = (4 + 0 + -25i2 + -2x + -2x + x2) y = (4 + -25i2 + -2x + -2x + x2) Combine like terms: -2x + -2x = -4x y = (4 + -25i2 + -4x + x2) Solving y = 4 + -25i2 + -4x + x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 4 + -25i2 + -4x + x2
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