## anonymous one year ago I need someone to explain this lesson to me. Be patient while I write the problem.

1. anonymous

Ok so it is walking me through the steps to solve for x $\sqrt{x+21}-3=\sqrt{x}$

2. anonymous

Here are the steps:$\sqrt{x+21}=3+\sqrt{x}$ $x+21=9+6\sqrt{x}+x$ $12=6\sqrt{x}$ $\sqrt{x}=2$ $x=4$

3. anonymous

The 2nd step is the one I didn't understand?$x+21=9+6\sqrt{x}+x$

4. UsukiDoll

ahhhh... they squared both sides.

5. UsukiDoll

because we want x... no x^2 stuff square root of x just x so we square both sides $(\sqrt{x+21})^2=(3+\sqrt{x})^2$

6. anonymous

Ok but wouldn't that leave us with $x+21=9+x$

7. UsukiDoll

the left side is correct.. the right one requires expansion

8. UsukiDoll

$(\sqrt{x+21})(\sqrt{x+21}) = (3+\sqrt{x})(3+\sqrt{x})$

9. UsukiDoll

so square root x square root is just whatever is in the square root so x+21 = (use foil method )

10. anonymous

Ohhh Ok I get it thank you because the OI of FOIL add together to get the $6\sqrt{x}$ thank you

11. UsukiDoll

yup

12. UsukiDoll

then what they did was shift that x to the left to eliminate it and the 9 is shifted to the left

13. UsukiDoll

then divide both sides by 6 afterwards square both sides again and x = 4

14. anonymous

Yeah I get it thanks I am really liking this site it's helpin me out a lot