how the fuck do you solve this?

first i found out that x can't be below -7 because than the root would be negative.
Than put the 5 on the other site.
Than i squarred it so i have (x-5)^2 <= root(x+7)
than i did abc-formula
and got 2 and 9

9 is right, but 2 is not
it should be -7 and 9 but what exactly tells me that it is those two numbers? I could just try setting in my -7 but i had no explanation why i took exactly the -7 and not some other number

how would you fully solve it?