To solve the quadratic equation \( 25x^2 - 20x = -4 \) by factoring using the perfect square trinomial pattern, we first rearrange the equation:
\[ 25x^2 - 20x + 4 = 0 \]
Now, we can rewrite the left side as a perfect square trinomial. Notice that:
\[ 25x^2 - 20x + 4 = (5x - 2)^2 \]
Now the equation becomes:
\[ (5x - 2)^2 = 0 \]
To solve for \( x \), we take the square root of both sides:
\[ 5x - 2 = 0 \]
Now we solve for \( x \):
\[ 5x = 2 \] \[ x = \frac{2}{5} \]
So the solution to the quadratic equation is:
\[ x = \frac{2}{5} \]
Thus, the correct response is:
x equals Start Fraction 2 over 5 End Fraction.