Answer
Observe the first two terms on the LHS,
$x^{2}+6x=x^{2}+2(x)(3)$
We wrote the second term in this form to be in line with the formula
$(a+b)^{2}=a^{2}+\fbox{$2ab $}+b^{2}$
So, our b is 3, and the missing $ b^{2}$ term equals $3^{2}=9$.
We now rewrite the equation by adding $+9 $ to both sides
$ x^{2}+6x+9+8= 9\quad $... recognize square, add $-8$
$(x+3)^{2}=9-8$
$(x+3)^{2}=1\qquad $... take the square root, $ x+3$ can be -1 or 1
$ x+3=\pm 1\qquad $... isolate x, subtract 3
$ x=-3\pm 1$
$ x=-4$ or $ x=-2$
Solution set =$ \{-4,-2\}$
Work Step by Step
Given above.
