What will you do with A after that?

Nothing.

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.