Tewtor.ai

When we solve a quadratic, we can first simplify the equation by dividing every term by the same non‑zero number.
In the problem

the coefficient of $x^{2}$ is $2$. Dividing the whole equation by $2$ gives a simpler, “monic’’ quadratic (one whose leading coefficient is 1):

Why do this?

1. Easier arithmetic – Smaller numbers mean fewer chances for arithmetic errors.

2. Factoring becomes straightforward – With a leading coefficient of 1, we look for two numbers that multiply to $c$ (here 3) and add to $b$ (here –4). Those numbers are $-1$ and $-3$, so

   $$x^{2}-4x+3=(x-1)(x-3)=0 .$$

3. The quadratic formula works either way, but the discriminant calculation is simpler when the coefficients are smaller.

If you prefer to keep the original coefficients, you can still apply the quadratic formula directly:

which leads to the same roots $x=1$ and $x=3$.

So dividing by 2 first is just a convenient shortcut; it doesn’t change the solutions, it only makes the algebra a bit cleaner.

If you’d like to see a visual comparison of solving the quadratic with and without that initial division, the video below walks through both approaches.