Solve the following equation:
$x^{3} - 18 x = 35$ .

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Solution

Given equation, $x^{3} - 18 x - 35 = 0$

$⟹ x^{3} + 5 x^{2} - 5 x^{2} + 7 x - 25 x - 35 = 0 ⟹ (x - 5) (x^{2} + 5 x + 7) = 0$

Solving the quadratic equation, we have $x = \frac{- 5 \pm \sqrt{3} i}{2}$

$∴$ roots of the given equation are $x = 5, \frac{- 5 \pm \sqrt{3} i}{2}$

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