SOLUTION: how to solve problem y+6square root y=16? they say the answer is 4, but i don't know how they came to that conclusion

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Question 145996: how to solve problem y+6square root y=16? they say the answer is 4, but i don't know how they came to that conclusion
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y+%2B6sqrt%28y%29+=+16
6sqrt%28y%29+=+16-y
Square both sides
36y = 256 - 32y + y^2}}}
y%5E2+-68y+%2B+256+=+0
Factor
(y - 4)(y - 64) = 0
y = 4, y = 64

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+%2B+6%2Asqrt%28y%29+=+16
I define a new variable to be z%5E2+=+y
Taking the square root of both sides, z+=0+%2B-sqrt%28y%29
Sustituting,
z%5E2+%2B+6z+-16+=+0
%28z+%2B+8%29%28z+-+2%29+=+0
z+=+-8
z+=+2
Putting z back in terms of y
-sqrt%28y%29+=+-8
y+=+64
and
sqrt%28y%29+=+2
y+=+4
Now I substitute these answers in the original equation
y+%2B+6%2Asqrt%28y%29+=+16
64+-+6%2A8+=+16
64+-+48+=+16
16+=+16
and
4+%2B+6%2A2+=+16
4+%2B+12+=+16
It looks like they are only allowing sqrt%28y%29 to be
positive, so y+=+4 and sqrt%28y%29+=+2 are the answers