求解二次方程$\sqrt{2}x^{2}+7x+5\sqrt{2}=0$的根。

已知：二次方程$\sqrt{2}x^{2}+7x+5\sqrt{2}=0$。

要求：求解该二次方程的根。

$\sqrt{2} x² +7x +5 \sqrt{2} = 0$

$\Rightarrow \sqrt{2} x² + 5x + 2x + 5\sqrt{2} = 0$

$\Rightarrow \sqrt{2}x²  + 5x + \sqrt{2}*\sqrt{2}*x + 5\sqrt{2}=0$

$\Rightarrow x(\sqrt{2}x + 5) + \sqrt{2}(\sqrt{2}x + 5) =0$

$\Rightarrow (x+\sqrt{2})(\sqrt{2}x+5) = 0$

$x= - \sqrt{2}\ 或\  x= - \frac{5}{\sqrt{2}}$