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