Is there a solution to 16^2-8x+1=0

If ya meant 16x²-8x+1=0 then
complete square
group x
(16x²-8x)+1=0
undistribute 16
16(x²-0.5x)+1=0
take 1/2 of linear coefient and squre positive and negaitve of it inside parentheasees
-0.5/2=-0.25, (-0.25)^2=0.0625
16(x²-0.5x+0.0625-0.0625)+1=0
factor perfect square trinomial
16((x-0.25)²-0.0625)+1=0
expand
16(x-0.25)²-1+1=0
16(x-0.25)²=0
(x-0.25)²=0
x-0.25=0
x=0.25

or, if you mean
16²-8x+1=0
256-8x+1=0
257-8x=0
add 8x both sides
257=8x
divide both sides by 8
257/8=x