(x+20)squared = 49
$\displaystyle (x+20)^2 = 49$
We can square root both sides.
If $\displaystyle x^2 = a$, then $\displaystyle |x| = \sqrt {a}$.
NOT $\displaystyle x = \sqrt {a}$ !!
So,
$\displaystyle (x+20)^2 = 49$
$\displaystyle |x+20| = \sqrt{49}$
$\displaystyle |x+20| = 7$
$\displaystyle x+20 = +7 $ and $\displaystyle x+20 = -7 $
$\displaystyle x+20 = +7 $
$\displaystyle x = -13$
$\displaystyle x+20 = -7 $
$\displaystyle x = -27 $
$\displaystyle x = \{-27,-13\}$