To solve the quadratic equation [tex]\(2x^2 - 7x + 3 = 0\)[/tex] by completing the square, the best first step is to divide the entire equation by 2. This simplifies the process of completing the square by making the coefficient of [tex]\(x^2\)[/tex] equal to 1.
Here's a detailed step-by-step reasoning:
1. Start with the given equation:
[tex]\[2x^2 - 7x + 3 = 0\][/tex]
2. Divide the entire equation by 2:
[tex]\[\frac{2x^2}{2} - \frac{7x}{2} + \frac{3}{2} = \frac{0}{2}\][/tex]
Simplifying this, we get:
[tex]\[x^2 - \frac{7}{2}x + \frac{3}{2} = 0\][/tex]
Now, the quadratic equation is in a form where completing the square is more manageable.
Thus, the best first step is to divide the entire equation by 2.
