Question

Solve the equation using quadratic formula.

$a^2-2a-15=0$

Short answer

The roots are $a=-3,a=5$

Step-by-step solution

 Given Information.  

The given equation is $a^2-2a-15=0$.

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

$a^2-2a-15=0$

The equation is in standard form.

So,

$a=1,b=-2,c=-15$

Substitute the values in quadratic formula. 

$$\begin{gathered} a=\frac{-(-2)\pm \sqrt{(-2{)}^2-4(1\left)\right(-15)}}{2\left(1\right)} \\ a=\frac{2\pm \sqrt{4+60}}{2} \\ a=\frac{2\pm \sqrt{64}}{2} \end{gathered}$$

Use square root property.  

$a=\frac{2\pm 8}{2}$

Rewrite to show two solutions.

$$\begin{gathered} a_1=\frac{2+8}{2} \\ {a}_1=\frac{10}{2} \\ {a}_1=5 \end{gathered}$$

and

$$\begin{gathered} a_2=\frac{2-8}{2} \\ {a}_2=\frac{-6}{2} \\ {a}_2=-3 \end{gathered}$$

Thus, the roots are$a=-3,a=5$.