Its going to be a lot of steps
Step one
To complete the square, the same value needs to be added to both sides
f(x)+?=x^2 -9x+?+14
Step two
To complete the square add to the expression
x^2 -9 + 81/4= ( x- 9/2 ) ^2 add 81/4
To the expression
f(x)+?=x^2 -9+ 81/4 + 14
Step three
Since 81/4 was added to the right-hand side, also add 81/4 to the left-hand side
f(x)+81/4=x^2 -9x+81/4+14
Step four
Use a^2-2ab +b^2 = ( a-b)^2 to factor the expression
f(x)+81/4=(x-9/2)^2+14
Step five
Move the constant to the right-hand side and change its sign
f(x)=(x-9/2)^2 + 14- 81/4
Last step
Calculate the difference
F(x)=(x-9/2)^2 -25/4
That was to long
Karl:D