Question

In the following exercises, solve by using the Quadratic Formula.
$25q^2+30q+9=0$

Short answer

The solution of the given equation is $q=-\frac{3}{5}$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$25q^2+30q+9=0$

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a{x}^2+bx+c=0$is:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In the given equation, $a=25,b=30,c=9$. Substitute these values in Quadratic Formula.

$q=\frac{-30\pm \sqrt{(30{)}^2-4(25\left)\right(9)}}{2\left(25\right)}$

Step 3. Simplify the value.

On simplification, we get

$$\begin{gathered} q=\frac{-30\pm \sqrt{900-900}}{50} \\ q=\frac{-30\pm 0}{50} \\ q=\frac{-30}{50} \\ q=-\frac{3}{5} \end{gathered}$$

Step 4. Conclusion.

The solution of the given equation is $q=-\frac{3}{5}$.