Q 292 - Intermediate Algebra

Question

In the following exercises, solve:

$64p^2=225$

Step-by-Step Solution

Answer

On solving the equation, we get $p=\frac{15}{8},-\frac{15}{8}$.

Step 1. Given information.

Consider the given equation,

$64p^2=225$

Write the quadratic equation in standard form,

$64p^2-225=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} {\left(8p\right)}^2-{\left(15\right)}^2=0 \\ \left(8p+15\right)\left(8p-15\right)=0 \end{gathered}$$

Use the zero product property,

$$\begin{gathered} 8p+15=0 \\ p=-\frac{15}{8} \end{gathered}$$

Then,

$$\begin{gathered} 8p-15=0 \\ p=\frac{15}{8} \end{gathered}$$

Step 3. Check the answers.

Substitute $p=\frac{15}{8}$ in the given equation,

$$\begin{gathered} 64{\left(\frac{15}{8}\right)}^2=225 \\ 64\times \frac{225}{68}=225 \\ 225=225 \end{gathered}$$

This is true.

Substitute $p=-\frac{15}{8}$ in the given equation,

$$\begin{gathered} 64{\left(-\frac{15}{8}\right)}^2=225 \\ 64\times \frac{225}{64}=225 \\ 225=225 \end{gathered}$$

This is also true.

Hence, the answer is $p=\frac{15}{8},-\frac{15}{8}$.