Question

√(x-2)=8-x

Answer 1

Square both side:
\[x-2=(8-x)^2\]
Expand terms:
\[x-2=x^2-16x+64\]
Put all on one side:
\[-x^2+17x-66=0\]
Factor:
\[-((x-11)(x-6))=0\]
Multiply both side by -1:
(x-11)(x-6)=0
Two Solutions: x=11 and x=6.

Plug them back into the original equation and see that the only correct solution is
\[x=6\]