Question

Solve by using the Quadratic Formula:$r^2+10r+25=0$

Short answer

The solution of the quadratic equation is $r=-5$

Step-by-step solution

Given information

We are given the quadratic equation$r^2+10r+25=0$

identify the values of a,b,c

On comparing with standard equation we get$a=1,b=10,c=25$

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$r=\frac{-10\pm \sqrt{100-4\left(1\right)\left(25\right)}}{2}$

Simplify 

On simplifying we get

$$\begin{gathered} r=\frac{-10\pm \sqrt{100-100}}{2} \\ r=\frac{-10}{2} \\ r=-5 \end{gathered}$$

Conclusion

The solution of the equation is$r=-5$