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

Aug 5th 2011, 12:04 PM

mathmathmathmathmathmathm

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

heres the orginal problem

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

Aug 5th 2011, 12:07 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

If you tidy that up a bit: $\displaystyle -6-2x = 2\sqrt{x+6} $

Aug 5th 2011, 06:45 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 $\displaystyle \displaystyle -6-2x = 4\sqrt{x} + 6$ or $\displaystyle \displaystyle -6-2x = 4\sqrt{x+6}$?

Aug 5th 2011, 08:10 PM

BERMES39

1 Attachment(s)

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

Try this,

Aug 5th 2011, 09:04 PM

SammyS

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

To avoid producing extraneous solutions I like the following method.

$\displaystyle -6-2x = 4\sqrt{x+6}$ , but first, divide both sides by 2 & get rid of the terms on the left side.

now add & subtract 6 at strategic locations: $\displaystyle 0 =x+6+2\sqrt{x+6}+3-6$

$\displaystyle 0 = (\sqrt{x+6})^2+2\sqrt{x+6}-3$

Now factor: $\displaystyle 0 = (\sqrt{x+6}+3)(\sqrt{x+6}-1)$

Since $\displaystyle \sqrt{x+6}\ne-3$, the only solution can be $\displaystyle \sqrt{x+6}=1\,.$

This gives x=-5 .

Aug 6th 2011, 04:58 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