When completing the square for a given polynomial in the form
$$Ax^2+Bx+C=0 $$
the first step is to ensure that $A =1$. If $A$ is not $1$ then you would divide each term by $A$ to get $A=1$.
I was given the equation $3x^2+6x+5=0$ and I decided to use the quadratic formula.
Now, for this equation
$a=3\quad b=6\quad c=5$
However, I divided the whole equation by $3$ to get $a=1 \quad b=2 \quad c=5/3 $
I proceeded to solve using the quadratic formula. This led me to an incorrect answer on my given test. Why? I, feeling idiotic, concluded that I had changed the original equations value by dividing by $3$. Then why is it that you can do such an operation when completing the square? Aren't you changing the equation as well? These kinds of mistakes really demotivate me because I want to master algebra but I feel inadequate every time stuff like this happens.
This is what I did and was marked incorrect for:
This is what my teacher did:
