Question

In the following exercises, solve each equation.

$7p^2+10=26$

Short answer

The solution of the equation is$p=4\sqrt{\frac{1}{7}},-4\sqrt{\frac{1}{7}}$

Step-by-step solution

Step 1. Given information

In the given question we have to solve given equation.
$7p^2+10=26$

Step 2. The given equation is 7p2+10=26

Isolate the quadratic term.

Subtract 10 on both side

$$\begin{gathered} 7p^2+10-10=26-10 \\ 7p^2=16 \end{gathered}$$

Divide by 7 on both side

$$\begin{gathered} \frac{7}{7}{p}^2=\frac{16}{7} \\ {p}^2=\frac{16}{7} \end{gathered}$$

Step 3. Use the Square Root Property.

$p=\pm \sqrt{\frac{16}{7}}$

Simplify the radical.

$p=\pm 4\sqrt{\frac{1}{7}}$

Step 4. Rewrite to show two solutions.

$p=4\sqrt{\frac{1}{7}}p=-4\sqrt{\frac{1}{7}}$