#### Answer

{$-4-\sqrt15$}, {$-4+\sqrt15$}
This above answer is written as a solution set, however it can also be written as:
$x=-4\pm\sqrt15$

#### Work Step by Step

Solve by completing the square.
$x^2+8x+1$
Take the c term to the other side.
$-1=x^2+8x$
Create a perfect square trinomial, and add the new c term to the other side as well.
$-1+16=x^2+8x+16$
Factor.
$15=(x+4)^2$
Solve.
$\sqrt(x+4)^2=\sqrt15$
$x=-4\pm\sqrt15$