lg^2 x + lg x^2 = lg^2 2 -1

lg^2 x+2lg x+1=lg^2 2
(lg x+1)^2=(lg 2)^2
lg x+1=lg 2
lg x=lg 2-1
lg x =lg 2 - lg 10
lg x= lg 2/10
x=2/10
x=1/5