To solve the quadratic equation \(25x^2 + 20x + 4 = 0\), we can use the quadratic formula, which is given by \(x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}\). Here, \(a = 25\), \(b = 20\), and \(c = 4\). We will calculate the discriminant \(b^2 - 4ac\) to determine the nature of the roots and then apply the formula to find the values of \(x\).
Step 1: Identify the Quadratic Equation
We start with the quadratic equation given by:
\[
25x^2 + 20x + 4 = 0
\]
Step 2: Calculate the Discriminant
The discriminant \(D\) is calculated using the formula:
\[
D = b^2 - 4ac
\]
Substituting the values \(a = 25\), \(b = 20\), and \(c = 4\):