TITLE: Completing the square for quadratic equation
QUESTION [7 upvotes]: I'm learning algebra (at age $66$) with home schooling materials. I am doing well and enjoying it. My question is this: The material says I can use "Completing the square" to solve any quadratic equation. I solved this equation 
$$6x^2+24x=0$$ 
by factoring (got answers $0$ and $-4$). But when I try and solve the same equation by completing the square I get a different answer ($\pm 12$). I must be doing something wrong but can't figure it out as I think I'm using the right steps to complete the square. Any help appreciated.

REPLY [2 votes]: From the comments: Your problem is the $a$ value in $ax^2+bx+c$. When you're completing the square, the conventional method of approach is to divide both sides by $a$, to get$$ax^2+bx+c=0\implies x^2+\dfrac bax+\dfrac ca=0\tag1$$
This reduces the leading coefficent (was $a$) down to $1$, and you can continue as before. Hence,$$\begin{align*} & 6x^2+24x=0\\ & \implies x^2+4x=0\\ & \implies x^2+4x+\left(\dfrac 42\right)^2=\left(\dfrac 42\right)^2\\ & \implies (x+2)^2=4\\ & \ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\end{align*}$$
And continue as before.


Something worth noting:

This is exactly how the quadratic formula can be found. Start with the general quadratic $ax^2+bx+c=0$ and divide both sides by $a$. Then complete the square, and solve for $x$.