## anonymous 3 years ago solve. sqrt(x+5)-1=sqrt(x)

1. anonymous

$\sqrt{x+5}-1=\sqrt{x}$

2. anonymous

$\sqrt{x + 5} - 1 = \sqrt{x}$

3. anonymous

Take 1 to the other side and square on both sides.

4. anonymous

ok so i got: $x+5=x+2\sqrt{x}+1$

5. anonymous

|dw:1345014199718:dw|

6. anonymous

then I subtract a x and the 1 from both sides?

7. anonymous

yep, you were faster than me. @TuringTest any ideas how to remove the square root?

8. anonymous

to isolate the squareroot? this is where I get lost every time..

9. anonymous

|dw:1345014331464:dw|

10. TuringTest

no I was mistake it goes away when you get rid of x and square both sides

11. anonymous

ok, i got this.

12. TuringTest

mistaken*

13. TuringTest

yes you do :)

14. anonymous

|dw:1345014366077:dw| done

15. anonymous

ok, then divide both sides by 2. then square both sides. thank you!

16. anonymous

welcome.

17. anonymous

could one of you give me a different problem that is still similar math?

18. anonymous

|dw:1345014658648:dw| same format, different terms.

19. anonymous

k. thank you. give me a minute to do it, then could you let me know if i did it right?

20. anonymous

sure.

21. anonymous

It will come as a negative fraction, don't bother simplifying.

22. anonymous

Its ok if the answer looks too complicated, I made up the question on the spot.

23. anonymous

i got 169/32=x

24. anonymous

|dw:1345015382310:dw| you made a mistake there.

25. anonymous

i thought when you divide a fraction by another fraction you are really just multiplying it by the reciprocal.

26. anonymous

ohh..... never mind... I get it 1/2 is the reciprocal of 2... duh.

27. anonymous

right.

28. anonymous

√(x+5) - 1 = √x √x + 1 = √(x+5) by squaring both sides, (√x + 1)² = [√(x + 5)]² (√x)² + 2 * √x * 1 + 1² = x + 5 x + 2√x + 1 = x + 5 2√x = 5 - 1 √x = 4/2 x = 2² x = 4