Final answer:
The quadratic equation 25x² + 20x + 4 = 0 is a perfect square trinomial and can be solved by factoring into (5x + 2)². Setting this factor to zero and solving for x gives the solution x = -2/5.
Step-by-step explanation:
The equation given is a quadratic equation, and it is already set to zero: 25x² + 20x + 4 = 0. We can try factoring it, but in this case, it appears to be a perfect square trinomial. The trinomial can be factored into (5x + 2)². The zero-factor property tells us that if a product equals zero, one or more of the factors must equal zero. Thus, we set the factor equal to zero and solve for x:
(5x + 2)^2 = 0
We take the square root of both sides:
5x + 2 = 0
Then solve for x:
5x = -2
x = -2/5
So, the solution to the equation is x = -2/5.