SOLUTION: please help me solve this equation: {{{ y=(y-2)^.5+2 }}} im confused because (y) is on both of the sides of the equation. please help.

Algebra ->  Exponents -> SOLUTION: please help me solve this equation: {{{ y=(y-2)^.5+2 }}} im confused because (y) is on both of the sides of the equation. please help.      Log On


   

Question 29769: please help me solve this equation: +y=%28y-2%29%5E.5%2B2+
im confused because (y) is on both of the sides of the equation. please help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y=%28y-2%29%5E.5%2B2+
subtract 2 from both sides
y+-+2+=+sqrt%28y+-+2%29
looking at this, it says something equals it's own square root
If I let y = 3, then
1+=+sqrt%281%29 which is true
If I let y = 2, then
0+=+sqrt%280%29 which is true
square both sides
%28y+-+2%29%5E2+=+y+-+2
y%5E2+-4%2Ay+%2B+4+=+y+-+2
y%5E2+-5%2Ay+%2B+6+=+0
factoring
%28y+-+2%29%2A%28y+-+3%29+=+0
This can be true if y = 2 or y = 3
which is what I saw by observation