heres the orginal problem
sqrt of 4 - x - sqrt of x + 6 = 2
-6 - 2x = 4 times sqrt of x + 6
this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
You can square both sides:
Solve for x and check for extraneous solutions using the original equation. Note that due to the domain
EDIT: Your equation in the OP is fine but there is an additional domain restriction
I've put the working to show this in a spoiler to keep the post more coherent.
Spoiler:
To avoid producing extraneous solutions I like the following method.
, but first, divide both sides by 2 & get rid of the terms on the left side.
Starting with:
now add & subtract 6 at strategic locations:
Now factor:
Since , the only solution can be
This gives x=-5 .