Question

Solve the equation using quadratic formula.

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

Short answer

The roots is$q=\frac{-3}{5}$.

Step-by-step solution

 Given Information.   

The given equation is$25q^2+30q+9=0$

Write the quadratic equation in standard form and identify a,b,c.

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

The equation is in standard form.

So,

$a=25,b=30,c=9$

Substitute the values in quadratic formula.   

$$\begin{gathered} q=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ q=\frac{-30\pm \sqrt{(30{)}^2-4(25\left)\right(9)}}{2\left(25\right)} \\ q=\frac{-30\pm \sqrt{900-900}}{50} \\ q=\frac{-30\pm \sqrt{0}}{50} \end{gathered}$$

Use square root property. 

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

There is only one solution,$q=\frac{-3}{5}$.