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Simplifying x2 + 4ix + 1 = 0 Reorder the terms: 1 + 4ix + x2 = 0 Solving 1 + 4ix + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4ix + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4ix + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4ix + x2 = 0 + -1 4ix + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4ix + x2 = -1 Add '-1x2' to each side of the equation. 4ix + x2 + -1x2 = -1 + -1x2 Combine like terms: x2 + -1x2 = 0 4ix + 0 = -1 + -1x2 4ix = -1 + -1x2 Divide each side by '4x'. i = -0.25x-1 + -0.25x Simplifying i = -0.25x-1 + -0.25x
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