SOLUTION: Hi, the equation is: X - 4*(square root X) = 32. I thought about squaring both sides to get a quadratic, but that would still leave a (square root of x) in the equation. Thanks

Question 829204: Hi, the equation is: X - 4*(square root X) = 32. I thought about squaring both sides to get a quadratic, but that would still leave a (square root of x) in the equation. Thanks for any help you can provide.
Found 2 solutions by edjones, KMST:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
x-4sqrt(x)=32
x-4sqrt(x)-32=0
(sqrt(x)-8)(sqrt(x)+4)=0
sqrt(x)=8
x=64
.
Ed
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If there is only one square root, you want to isolate it on one side of the equation before squaring.

or
Also, if has to be a real number, it must be that .
Now we can square both sides, knowing that we may be introducing some exraneous solutions.

Factoring, since , we transform the equation into
, whose solutions are
and
Is any one of those an extraneous solution?
For ,
so is not a solution of the original equation. It's an extraneous solution, introduced when we squared both sides.
For ,
So is a solution to the original equation.
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