Question

Find the roots of the quadratic equation:
$\sqrt{2} x^{2} +7x + 5 \sqrt{2} =0$

Answer 1

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