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Simplifying (x + -1(5 + -8i))(x + -1(5 + 8i)) = 0 (x + (5 * -1 + -8i * -1))(x + -1(5 + 8i)) = 0 (x + (-5 + 8i))(x + -1(5 + 8i)) = 0 Reorder the terms: (-5 + 8i + x)(x + -1(5 + 8i)) = 0 (-5 + 8i + x)(x + (5 * -1 + 8i * -1)) = 0 (-5 + 8i + x)(x + (-5 + -8i)) = 0 Reorder the terms: (-5 + 8i + x)(-5 + -8i + x) = 0 Multiply (-5 + 8i + x) * (-5 + -8i + x) (-5(-5 + -8i + x) + 8i * (-5 + -8i + x) + x(-5 + -8i + x)) = 0 ((-5 * -5 + -8i * -5 + x * -5) + 8i * (-5 + -8i + x) + x(-5 + -8i + x)) = 0 ((25 + 40i + -5x) + 8i * (-5 + -8i + x) + x(-5 + -8i + x)) = 0 (25 + 40i + -5x + (-5 * 8i + -8i * 8i + x * 8i) + x(-5 + -8i + x)) = 0 Reorder the terms: (25 + 40i + -5x + (-40i + 8ix + -64i2) + x(-5 + -8i + x)) = 0 (25 + 40i + -5x + (-40i + 8ix + -64i2) + x(-5 + -8i + x)) = 0 (25 + 40i + -5x + -40i + 8ix + -64i2 + (-5 * x + -8i * x + x * x)) = 0 Reorder the terms: (25 + 40i + -5x + -40i + 8ix + -64i2 + (-8ix + -5x + x2)) = 0 (25 + 40i + -5x + -40i + 8ix + -64i2 + (-8ix + -5x + x2)) = 0 Reorder the terms: (25 + 40i + -40i + 8ix + -8ix + -64i2 + -5x + -5x + x2) = 0 Combine like terms: 40i + -40i = 0 (25 + 0 + 8ix + -8ix + -64i2 + -5x + -5x + x2) = 0 (25 + 8ix + -8ix + -64i2 + -5x + -5x + x2) = 0 Combine like terms: 8ix + -8ix = 0 (25 + 0 + -64i2 + -5x + -5x + x2) = 0 (25 + -64i2 + -5x + -5x + x2) = 0 Combine like terms: -5x + -5x = -10x (25 + -64i2 + -10x + x2) = 0 Solving 25 + -64i2 + -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 + -64i2 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -64i2 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -64i2 + -10x + x2 = 0 + -25 -64i2 + -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -64i2 + -10x + x2 = -25 Add '10x' to each side of the equation. -64i2 + -10x + 10x + x2 = -25 + 10x Combine like terms: -10x + 10x = 0 -64i2 + 0 + x2 = -25 + 10x -64i2 + x2 = -25 + 10x Add '-1x2' to each side of the equation. -64i2 + x2 + -1x2 = -25 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 -64i2 + 0 = -25 + 10x + -1x2 -64i2 = -25 + 10x + -1x2 Divide each side by '-64'. i2 = 0.390625 + -0.15625x + 0.015625x2 Simplifying i2 = 0.390625 + -0.15625x + 0.015625x2 Reorder the terms: -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.390625 + -0.15625x + 0.015625x2 + -0.390625 + 0.15625x + -0.015625x2 Reorder the terms: -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.390625 + -0.390625 + -0.15625x + 0.15625x + 0.015625x2 + -0.015625x2 Combine like terms: 0.390625 + -0.390625 = 0.000000 -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.000000 + -0.15625x + 0.15625x + 0.015625x2 + -0.015625x2 -0.390625 + i2 + 0.15625x + -0.015625x2 = -0.15625x + 0.15625x + 0.015625x2 + -0.015625x2 Combine like terms: -0.15625x + 0.15625x = 0.00000 -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.00000 + 0.015625x2 + -0.015625x2 -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.015625x2 + -0.015625x2 Combine like terms: 0.015625x2 + -0.015625x2 = 0.000000 -0.390625 + i2 + 0.15625x + -0.015625x2 = 0.000000 The solution to this equation could not be determined.
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