Answer :

[tex]x^2+9=0\\ x^2=-9\\ x=\sqrt{-9} \vee x=-\sqrt{-9}\\ x=\sqrt{-1\cdot9} \vee x=-\sqrt{-1\cdot9}\\ x=\sqrt{-1}\cdot\sqrt9 \vee x=-\sqrt{-1}\cdot \sqrt9\\ x=i\cdot3 \vee -i\cdot3\\ x=3i \vee x=-3i [/tex]