Solving for x with a Square Root Sign: Help Needed!

[Jules18]

Does anyone know how to solve for x in the following equation:

x + \sqrt{x} = 6

I don't know how to solve for x with eq'ns like this, and I'm studying inverse fxns right now, so I'm told that's what I'm supposed to do.

The square root sign is throwing me off.
The first time I tried, I tried squaring both sides to get rid of the sq. root sign, but it just made it more complicated.
Any suggestions?

~Jules~

 

[emyt]

you need to isolate the sqrt(x), it will make everything A LOT nicer looking

 

[owlpride]

Try substituting u = sqrt(x).

 

[lurflurf]

It is a quadradic in sqrt(x)
factorize into the form
x+sqrt(x)-6=(a*sqrt(x)+b)(c*sqrt(x)+d)

 

[HallsofIvy]

Three basically different methods, all of which work! I would prefer emyt's method:
write the equation as \sqrt{x}= 6- x and square both sides. Caution: squaring both sides of an equation (or, more generally, multiplying both sides of an equation by something involving the unknown) can introduce "spurious roots" so be sure to check any solution in the original equation.