To solve the quadratic equation 25x^2 + 20x + 4 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 25, b = 20, and c = 4.

Plugging these values into the quadratic formula, we get:

x = (-20 ± √(20^2 - 4 * 25 * 4)) / (2 * 25)

Simplifying further:

x = (-20 ± √(400 - 400)) / 50

x = (-20 ± √0) / 50

Since the discriminant (√(b^2 - 4ac)) is equal to 0, there is only one real solution for x.

x = -20 / 50

Simplifying:

x = -2/5

Therefore, the solution to the quadratic equation 25x^2 + 20x + 4 = 0 is x = -2/5.