SOLUTION: Solve √x(2+√x) = 35.

Introduce new variable  y = .


Then the given equation takes the form


    y*(2+y) = 35.


To solve it formally, reduce it to the standard form of a quadratic equation or by factoring.


Also, the roots can be easily guessed MENTALLY.


In any case, the roots of equation (1)  are  y = 5  or  y = -7.


Since we admit only positive values for square roots, the original equation has only one solution x = 5^2 = 25.    ANSWER