solving equations w/ radicals and exponents problem, stuck

-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

August 5th 2011, 01:04 PM

mathmathmathmathmathmathm

Re: solving equations w/ radicals and exponents problem, stuck

heres the orginal problem

sqrt of 4 - x - sqrt of x + 6 = 2

August 5th 2011, 01:07 PM

e^(i*pi)

Re: solving equations w/ radicals and exponents problem, stuck

Quote:

Originally Posted by mathmathmathmathmathmathm

-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:

Quote:

Originally Posted by mathmathmathmathmathmathm

heres the orginal problem

If you tidy that up a bit:

August 5th 2011, 07:45 PM

Prove It

Re: solving equations w/ radicals and exponents problem, stuck

Quote:

Originally Posted by mathmathmathmathmathmathm

-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

Is your equation or ?

August 5th 2011, 09:10 PM

BERMES39

1 Attachment(s)

Re: solving equations w/ radicals and exponents problem, stuck

Try this,

August 5th 2011, 10:04 PM

SammyS

Re: solving equations w/ radicals and exponents problem, stuck

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 .

August 6th 2011, 05:58 AM

mrmohamed

1 Attachment(s)

Re: solving equations w/ radicals and exponents problem, stuck

Quote:

Originally Posted by mathmathmathmathmathmathm

-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