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Simplifying (x + -3 + 4i)(x + -3 + -4i) = 0 Reorder the terms: (-3 + 4i + x)(x + -3 + -4i) = 0 Reorder the terms: (-3 + 4i + x)(-3 + -4i + x) = 0 Multiply (-3 + 4i + x) * (-3 + -4i + x) (-3(-3 + -4i + x) + 4i * (-3 + -4i + x) + x(-3 + -4i + x)) = 0 ((-3 * -3 + -4i * -3 + x * -3) + 4i * (-3 + -4i + x) + x(-3 + -4i + x)) = 0 ((9 + 12i + -3x) + 4i * (-3 + -4i + x) + x(-3 + -4i + x)) = 0 (9 + 12i + -3x + (-3 * 4i + -4i * 4i + x * 4i) + x(-3 + -4i + x)) = 0 Reorder the terms: (9 + 12i + -3x + (-12i + 4ix + -16i2) + x(-3 + -4i + x)) = 0 (9 + 12i + -3x + (-12i + 4ix + -16i2) + x(-3 + -4i + x)) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + (-3 * x + -4i * x + x * x)) = 0 Reorder the terms: (9 + 12i + -3x + -12i + 4ix + -16i2 + (-4ix + -3x + x2)) = 0 (9 + 12i + -3x + -12i + 4ix + -16i2 + (-4ix + -3x + x2)) = 0 Reorder the terms: (9 + 12i + -12i + 4ix + -4ix + -16i2 + -3x + -3x + x2) = 0 Combine like terms: 12i + -12i = 0 (9 + 0 + 4ix + -4ix + -16i2 + -3x + -3x + x2) = 0 (9 + 4ix + -4ix + -16i2 + -3x + -3x + x2) = 0 Combine like terms: 4ix + -4ix = 0 (9 + 0 + -16i2 + -3x + -3x + x2) = 0 (9 + -16i2 + -3x + -3x + x2) = 0 Combine like terms: -3x + -3x = -6x (9 + -16i2 + -6x + x2) = 0 Solving 9 + -16i2 + -6x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -16i2 + -6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -16i2 + -6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -16i2 + -6x + x2 = 0 + -9 -16i2 + -6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -16i2 + -6x + x2 = -9 Add '6x' to each side of the equation. -16i2 + -6x + 6x + x2 = -9 + 6x Combine like terms: -6x + 6x = 0 -16i2 + 0 + x2 = -9 + 6x -16i2 + x2 = -9 + 6x Add '-1x2' to each side of the equation. -16i2 + x2 + -1x2 = -9 + 6x + -1x2 Combine like terms: x2 + -1x2 = 0 -16i2 + 0 = -9 + 6x + -1x2 -16i2 = -9 + 6x + -1x2 Divide each side by '-16'. i2 = 0.5625 + -0.375x + 0.0625x2 Simplifying i2 = 0.5625 + -0.375x + 0.0625x2 Reorder the terms: -0.5625 + i2 + 0.375x + -0.0625x2 = 0.5625 + -0.375x + 0.0625x2 + -0.5625 + 0.375x + -0.0625x2 Reorder the terms: -0.5625 + i2 + 0.375x + -0.0625x2 = 0.5625 + -0.5625 + -0.375x + 0.375x + 0.0625x2 + -0.0625x2 Combine like terms: 0.5625 + -0.5625 = 0.0000 -0.5625 + i2 + 0.375x + -0.0625x2 = 0.0000 + -0.375x + 0.375x + 0.0625x2 + -0.0625x2 -0.5625 + i2 + 0.375x + -0.0625x2 = -0.375x + 0.375x + 0.0625x2 + -0.0625x2 Combine like terms: -0.375x + 0.375x = 0.000 -0.5625 + i2 + 0.375x + -0.0625x2 = 0.000 + 0.0625x2 + -0.0625x2 -0.5625 + i2 + 0.375x + -0.0625x2 = 0.0625x2 + -0.0625x2 Combine like terms: 0.0625x2 + -0.0625x2 = 0.0000 -0.5625 + i2 + 0.375x + -0.0625x2 = 0.0000 The solution to this equation could not be determined.
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