take 1/2 of linear coefient and square it
18 is linear coefient so 18/2=9, 9^2=81
add that to both sides
[tex]x^2+18x+81=125[/tex]
factor perfect square trionomial
[tex](x+9)^2=125[/tex]
there, completed the square
if you want to solvesquare root both sides, don't forget positive and negative roots
[tex]x+9=\pm \sqrt{125}[/tex]
[tex]x=-9 \pm 5\sqrt{5}[/tex]
[tex]x=-9+5\sqrt{5}[/tex] and [tex]x=-9-5\sqrt{5}[/tex]
