Rewrite by completing the square.x2 + 3x + 1

To rewrite the expression x^2 + 3x + 1 by completing the square, follow these steps:

1. Separate the constant term: x^2 + 3x + 1 becomes (x^2 + 3x) + 1

2. In the quadratic part (x^2 + 3x), take half of the coefficient of x, square it, and add and subtract it inside the parenthesis. Half of 3 is 1.5, and 1.5^2 = 2.25. So, we get (x^2 + 3x + 2.25 - 2.25) + 1

3. Now, the first three terms inside the parenthesis form a perfect square: (x + 1.5)^2 - 2.25 + 1

4. Simplify the constants: (x + 1.5)^2 - 1.25

So, x^2 + 3x + 1 can be rewritten as (x + 1.5)^2 - 1.25 by completing the square.