got the following inequation sequence:

$-10 \leq x \leq 12 \Leftrightarrow$
$-10+5 \leq x+5 \leq 12+5 \Leftrightarrow$
$(-5)^2 \leq (x+5)^2 \leq 17^2 \Leftrightarrow$
$25+3 \leq (x+5)^2+3 \leq 289+3 <br /> \Leftrightarrow$
$28 \leq (x+5)^2+3 \leq 292$

I'm thinking that the error here is that, when you start to do $(x+5)^2+3 \leq 292$ you eventually end up in $x^2+10x \leq 264$ which is a quadratic inequation, therefore it gives you two values for $x$, is this correct?

if not, pls explain i'm a brainlet