Questions: Solve. 25 x^2+20 x+4=0 x=

Solution Steps

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 \(x\).

We start with the quadratic equation given by:

\[ 25x^2 + 20x + 4 = 0 \]

The discriminant \(D\) is calculated using the formula:

\[ D = b^2 - 4ac \]

Substituting the values \(a = 25\), \(b = 20\), and \(c = 4\):

\[ D = 20^2 - 4 \cdot 25 \cdot 4 = 400 - 400 = 0 \]

Since the discriminant \(D = 0\), there is exactly one real root (a repeated root). We can find the root using the quadratic formula:

\[ x = \frac{{-b \pm \sqrt{D}}}{2a} \]

Substituting \(D = 0\):

\[ x = \frac{{-20 \pm 0}}{2 \cdot 25} = \frac{{-20}}{50} = -0.4 \]

Final Answer