To find the minimum value of the given expression (2x^2 + 5x + 7), we can use the concept of completing the square.

Completing the square involves rewriting the quadratic expression in a perfect square form, which allows us to determine the minimum value of the quadratic function.

Let's solve this step by step:

Step 1: Identify the coefficients of the quadratic expression.
- a = 2
- b = 5
- c = 7

Step 2: Rewrite the quadratic expression by completing the square.
- Start by taking half of the coefficient of x and squaring it: (5/2)^2 = 25/4.
- Add and subtract this value within the expression:
(2x^2 + 5x + 25/4 - 25/4 + 7).
- Rearrange the expression: (2x^2 + 5x + 25/4 - 25/4 + 7) = (2x^2 + 5x + 25/4) - 25/4 + 7.
- Simplify the expression: (2x^2 + 5x + 25/4) - 25/4 + 7 = (2x^2 + 5x + 25/4) + 23/4.

Step 3: Rewrite the quadratic expression as a perfect square trinomial.
- Rewrite the expression: (2x^2 + 5x + 25/4) + 23/4 = (2x^2 + 5x + (5/2)^2) + 23/4.
- Factor the perfect square trinomial: (2x + 5/2)^2 + 23/4.

Step 4: Determine the minimum value of the quadratic function.
- Since the square of a real number is always positive or zero, the minimum value occurs when the perfect square trinomial is equal to zero.
- Set (2x + 5/2)^2 = 0 and solve for x: (2x + 5/2) = 0.
- Simplify and solve for x: 2x + 5/2 = 0 → 2x = -5/2 → x = -5/4.
- Substituting this value into the quadratic expression:
(2(-5/4)^2 + 5(-5/4) + 7) = 25/8 - 25/4 + 7 = 31/8.

Therefore, the minimum value of the expression (2x^2 + 5x + 7) is 31/8, which corresponds to option A.