Find the roots of the following quadratic equation by factorisation :

$\sqrt{2}x^2 +7x + 5\sqrt{2} = 0$

Solving,

$\Rightarrow \sqrt{2}x^2 + 7x + 5\sqrt{2} = 0 \\[1em] \Rightarrow \sqrt{2}x^2 + 2x + 5x + 5\sqrt{2} = 0 \\[1em] \Rightarrow \sqrt{2}x(x + \sqrt{2}) + 5(x + \sqrt{2}) = 0 \\[1em] \Rightarrow (\sqrt{2}x + 5)(x + \sqrt{2}) = 0 \\[1em] \Rightarrow \sqrt{2}x + 5 = 0 \text{ or } x + \sqrt{2} = 0 \\[1em] \Rightarrow \sqrt{2}x = -5 \text{ or } x = -\sqrt{2} \\[1em] \Rightarrow x = -\dfrac{5}{\sqrt{2}} \text{ or } x = -\sqrt{2}.$

Hence, x = $-\dfrac{5}{\sqrt{2}}\text{ or x} = -\sqrt{2}$.