#### Answer

$x = (-4-\sqrt 17, -4+\sqrt 17)$

#### Work Step by Step

Step -1 : Add the square of half of the co-efficient of x to both sides.
Co-efficient of x = 8
Half of 8 = $\frac{1}{2}\times8 = 4$
Square of 4 is $4 \times4 = 16$
The equation becomes $x^2+8x+16=1 +16$
Step-2 Factor the trinomial and simplify the right hand side.
$(x+4)^2= 17$
Step-3 Use the square root property and solve for $x$
$x+4=±\sqrt 17$
Step-4 Subtract 4 on both the sides
$x=-4±\sqrt 17$
Therefore the solution set is $(-4-\sqrt 17, -4+\sqrt 17)$