Question

Solve the quadratic equation by quadratic formula .$t^2+13t+22=0$

Short answer

The required result is$t=-11,-2$

Step-by-step solution

 Given Information 

The given equation is $t^2+13t+22=0$

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

The quadratic equation is in standard form.

So,

$a=1,b=13,c=22$

Substitute the values in quadratic formula.

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

$$\begin{gathered} t=\frac{-13\pm \sqrt{{\left(13\right)}^2-4\left(1\right)\left(22\right)}}{2\left(1\right)} \\ t=\frac{-13\pm \sqrt{169-88}}{2} \\ t=\frac{-13\pm \sqrt{81}}{2} \\ t=\frac{-13\pm 9}{2} \end{gathered}$$

We can write it as

$$\begin{gathered} t=\frac{-13-9}{2},\frac{-13+9}{2} \\ t=\frac{-22}{2},\frac{-4}{2} \\ t=-11,-2 \end{gathered}$$