Answer
$$x=8,\:x=3$$
Work Step by Step
We solve the equation using the rules of exponents and radicals. Note, if we wanted to check our solution, we could plug the value we get back into the original equation to see if it yields a true statement. Solving the equation, we find:
$$\left(\sqrt{21x+1}\right)^2=\left(x+5\right)^2\\ 21x+1=x^2+10x+25 \\ x=8,\:x=3$$
Checking for extraneous solutions, we see that neither solution is extraneous.
