Solve the given quadratic equation by factorisation method, $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$

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Solution

$\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$
$\Rightarrow \sqrt{2} x^{2} + 2 x + 5 x + 5 \sqrt{2} = 0$
$\Rightarrow \sqrt{2} x (x + \sqrt{2}) + 5 (x + \sqrt{2}) = 0$
$\Rightarrow (\sqrt{2} x + 5) (x + \sqrt{2}) = 0$
So $x = - \sqrt{2}$ or $x = \frac{- 5}{\sqrt{2}}$ .

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