What will you do with A after that?
And you so you cannot continue with your purpose.
In "completing the square", make sure first that the coefficient of the x^2 is unity or 1.
You have Ax^2.
You need to make that into x^2 only, before you continue.
So you divide Ax^2 by A,
Ax^2 / A = x^2 ----now you can continue.
Ax^2 +Bx +C^2 = 0
Divide both sides by A,
x^2 +(B/A)x +(C^2)/A = 0
Then go ahead with your com[leting the square.
Let me continue it.
x ^2 +(B/A)x = -(C^2)/A
x^2 +(B/A)x +[(B/A)/2]^2 = -(C^2)/A +[(B/A)/2]^2
x^2 +(B/A)x +(B/2A)^2 = -(C^2)/A +(B/2A)^2
Factor the Left side,
(x +B/2A)^2 = -(C^2)/A +(B/2A)^2
That is it.