Solve for X. Check for extraneous answers.
sqrt{x + sqrt{2x}}=sqrt{2}

Question

Solve for X. Check for extraneous answers.
sqrt{x + sqrt{2x}}=sqrt{2}

anonymous · Answer

square both sides get 
$$x+\sqrt{2x}=2$$ subtract $x$ from both sides and square again 
$$\sqrt{2x}=2-x$$
$$2x=(2-x)^2=4-4x+x^2$$

anonymous · Answer

then set equal to zero and solve the quadratic 
$$x^2-4x+4=2x$$
$$x^2-6x+4=0$$

anonymous · Answer

would x= 2?

anonymous · Answer

oh no you have to either use the quadratic formula or complete the square

anonymous · Answer

and you also have to check your answer 
$$x^2-6x=-4$$
$$(x-3)^2=-4+9=5$$
$$x-3=\pm\sqrt5]$$
$$x=3\pm\sqrt5$$

anonymous · Answer

now you have to check them
it will turn out that $3-\sqrt5$ works, while $3+\sqrt5$ does not

anonymous · Answer

Thank you very much! Without you, I would have been stuck on this question for the whole night! Thank you!