x √(x+(√x-2)=2

I believe this is supposed to  be  x √(x+(√x-2))=2

x √(x+(√x-2))= 2   divide both sides by x

√(x+(√x-2))  = 2/x  squre both sides

x + √x  - 2  =  4/x^2

√x  = 4/x^2  - x  + 2   

√x  = [ 4 - x^3  + 2x^2] / x^2      multiply both sides by x^2

x^(5/2)  = 4 - x^3 + 2x^2

x^3 + x^(5/2) -2x^2 - 4  = 0     

WolframAlpha shows the solution to this as   x ≈ 1.83436