We need to solve the following equation by completing the square:
[tex]x^2-4x-9=0[/tex]we first pass the 9 to sum in the right side
[tex]x^2-4x=9[/tex]now we add 4 in both sides of the equation, because (4/2)^2=4, obtaining
[tex]x^2-4x+4=9+4[/tex]simplifying
[tex](x-2)^2=13[/tex]then
[tex](x-2)=\pm\sqrt[]{13}[/tex]adding 2 in both sides of the equation we have that the solution is:
[tex]x=2\pm\sqrt[]{13}[/tex]