Answer
The solution is $p=7$.
Work Step by Step
The given equation is
$\Rightarrow p+1=\sqrt{7p+15}$
Square each side of the equation.
$\Rightarrow (p+1)^2=(\sqrt{7p+15})^2$
Simplify.
$\Rightarrow p^2+2p+1=7p+15$
Add $-7p-15$ to each side.
$\Rightarrow p^2+2p+1-7p-15=7p+15-7p-15$
Simplify.
$\Rightarrow p^2-5p-14=0$
Factor.
$\Rightarrow (p-7)(p+2)=0$
Use zero product property.
$\Rightarrow p-7=0$ or $p+2=0$
Solve for $p$.
$\Rightarrow p=7$ or $p=-2$
Check $p=7$.
$\Rightarrow p+1=\sqrt{7p+15}$
$\Rightarrow 7+1=\sqrt{7(7)+15}$
$\Rightarrow 8=\sqrt{49+15}$
$\Rightarrow 8=\sqrt{64}$
$\Rightarrow 8=8$
True.
Check $p=-2$.
$\Rightarrow p+1=\sqrt{7p+15}$
$\Rightarrow -2+1=\sqrt{7(-2)+15}$
$\Rightarrow -1=\sqrt{-14+15}$
$\Rightarrow -1=\sqrt{1}$
$\Rightarrow -1=1$
False
Hence, the solution is $p=7$.
