Question

plz help me for this question​

Answer 1

           

$\Rightarrow\ x^2+3x+1=0 \\ \\ \Rightarrow\ x^2+3x=-1 \\ \\ \Rightarrow\ x^2+3x+\frac{9}{4}=-1+\frac{9}{4} \\ \\ \Rightarrow\ (x+\frac{3}{2})^2=\frac{5}{4} \\ \\ \Rightarrow\ x+\frac{3}{2}=\pm\sqrt{\frac{5}{4}} \\ \\ \Rightarrow\ x+\frac{3}{2}=\pm\frac{\sqrt{5}}{2} \\ \\ \Rightarrow\ x=\pm\frac{\sqrt{5}}{2}-\frac{3}{2} \\ \\ \Rightarrow\ x=\bold{\frac{\sqrt{5}-3}{2}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{ OR }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=\bold{\frac{-\sqrt{5}-3}{2}}$

$\sf{Hope this helps. Plz ask me if you've any doubts. \\ \\ \\ Thank you. :-))}$