## anonymous 5 years ago √(x+4)-√(x+1)=1

1. anonymous

trying to solve for x?

2. anonymous

the answer is supposed to be x=0 but I don't know why

3. anonymous

Move one radical to the other side of the equation and then square each side. Remember that the right side will be a binomial so you will need to FOIL it. You will get a radical in the product so you will need to isolate it and solve it the same way by squaring each side.

4. anonymous

so when you move the radical over, your new equation is: √(x+4)=1+√(x+1)

5. anonymous

Yup. Now square each side. FOIL the right side.

6. anonymous

the left side just "pops" out as x+4?

7. anonymous

yes. lovely isn't it?

8. anonymous

yes, I'm making it overly complicated.

9. anonymous

you'll get this and then combine like terms and isolate the radical again. $x+4=x+1+2\sqrt{(x+1)} + 1$

10. anonymous

I'm afraid you lost me again.

11. anonymous

This is what you get when you square both sides.

12. anonymous

but then if you tried to get stuff over on the left, your x disappears...

13. anonymous

It's OK because you still have one under the radical. Did you get $2=2\sqrt{(x+1)}$

14. anonymous

yes, then do you get 4=4(x+1)?

15. anonymous

I would've divided both sides by 2 first, but you'll still get x=0 in the end.

16. anonymous

alright, let me try it that way then...I did not get to 0....

17. anonymous

YES!! Got it! Thank you so much for the step by step!!

18. anonymous

After dividing both sides by 2, you'll get $1=\sqrt{(x+1)}$

19. anonymous

YAY! Good luck!

20. anonymous

Lifesaver!