F4 Math find real root(s)

2(x-2)^0.5 + x = 10
2(x-2)^0.5 + x-2 = 10 - 2
2(x-2)^0.5 + (x-2) = 8
Let k be (x-2)^0.5 :
2k + k^2 = 8
k^2 + 2k - 8 = 0
(k - 2)(k + 4) = 0
k = (x-2)^0.5 = 2
x-2 = 4
x = 6
or k = (x-2)^0.5 = - 4 (rejected)