Answer: [tex]x_1=-1+2i\sqrt{2}}}\\\\x_2=-1-2i\sqrt{2}}[/tex]Step-by-step explanation: Use que Quadratic formula: [tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex] Given the quadratic equation [tex]x^2 + 2x + 9 = 0[/tex], you can identify that: [tex]a=1\\ b=2\\ c=9[/tex] Then, substitute values into the quadratic formula and simplify. Remember that [tex]\sqrt{-1}=i[/tex] Then: [tex]x=\frac{-2\±\sqrt{2^2-4(1)(9)}}{2(1)}[/tex] [tex]x=\frac{-2\sqrt{-32}}{2}[/tex] [tex]x=\frac{-2\±4i\sqrt{2}}{2}\\\\x=\frac{2(-1\±2i\sqrt{2})}{2}\\\\\\x_1=-1+2i\sqrt{2}}}\\\\x_2=-1-2i\sqrt{2}}[/tex]