this is wrong. you have x^2 = 7, not x = 7
you didn't write x^2 on the right the first time. make sure you are doing the right thing. should it be x^2 or x?And the second one turns into
1 - 2x = 1 + x^2
-1 = -1
-----------------
-2x = x^2
divide both by 2
-2 = x
no solution