Q. 429 - Intermediate Algebra

Question

In the following exercises, solve. 

$2p^2-11p=40$

Step-by-Step Solution

Answer

Answer is $p=8,p=-\frac{5}{2}$

Step 1. Given

The quadratic equation is $2p^2-11p=40$

Step 2. Simplify the quadratic equation

$$\begin{gathered} 2p^2-11p=40 \\ 2p^2-11p-40=0 \\ 2p^2-16p+5p-40=0 \\ 2p(p-8)+5(p-8)=0 \\ (p-8)(2p+5)=0 \end{gathered}$$

So,

$$\begin{gathered} p-8=0 \\ p=8 \end{gathered}$$

and

$$\begin{gathered} 2p+5=0 \\ p=-\frac{5}{2} \end{gathered}$$

Step 3. Check both the values

Put $p=8$ in original equation,

$$\begin{gathered} 2p^2-11p=40 \\ 2{\left(8\right)}^2-11\left(8\right)=40 \\ 128-88=40 \\ 40=40 \end{gathered}$$

Now put $p=-\frac{5}{2}$ in original equation,

$$\begin{gathered} 2p^2-11p=40 \\ 2{\left(-\frac{5}{2}\right)}^2-11\left(-\frac{5}{2}\right)=40 \\ \frac{25}{2}+\frac{55}{2}=40 \\ \frac{80}{2}=40 \\ 40=40 \end{gathered}$$

Step 4. Required answer

Answer is $p=8,p=-\frac{5}{2}$