To solve the quadratic equation $2x^2 - 7x + 3 = 0$ by completing the square, the best first step is to divide the entire equation by 2. This simplifies the coefficient of $x^2$ to 1, which is necessary when completing the square.

So, the correct answer is:

Divide the entire equation by 2.

Would you like more details on the process of completing the square, or have any further questions?

Here are 5 related questions that expand on this topic:

1. What is the general formula for completing the square for any quadratic equation?
2. How does dividing by a coefficient affect the process of completing the square?
3. Can you complete the square for a quadratic equation if the coefficient of $x^2$ is not 1?
4. What are the advantages of using the completing the square method over factoring?
5. How is completing the square used to derive the quadratic formula?

Tip: When completing the square, always make sure that the coefficient of $x^2$ is 1 before proceeding with the method.