Question

Solve the equation using quadratic formula.

$2p^2+8p+5=0$

Short answer

The roots are$p=\frac{-4+\sqrt{6}}{2},p=\frac{-4-\sqrt{6}}{2}$.

Step-by-step solution

 Given Information.  

The given equation is $2p^2+8p+5=0$.

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

$2p^2+8p+5=0$

The equation is in standard form.

So,

$a=2,b=8,c=5$

Substitute the values in quadratic formula.      

$$\begin{gathered} p=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ p=\frac{-8\pm \sqrt{(8{)}^2-4(2\left)\right(5)}}{2\left(2\right)} \\ p=\frac{-8\pm \sqrt{64-40}}{4} \\ p=\frac{-8\pm \sqrt{24}}{4} \end{gathered}$$

Use square root property.  

$p=\frac{-8\pm 2\sqrt{6}}{4}$

Simplify.

$p=\frac{-4\pm \sqrt{6}}{2}$

Rewrite to show two solutions.

$$\begin{gathered} p=\frac{-4+\sqrt{6}}{2}, \\ p=\frac{-4-\sqrt{6}}{2} \end{gathered}$$