Answer
$k=8$.
Work Step by Step
The given polynomial is
$\Rightarrow k^2-16k+64=0$
Write the the polynomial as $a^2-2ab+b^2$.
$\Rightarrow k^2-2(k)(8)+8^2=0$.
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$.
We have $a=k$ and $b=8$.
$\Rightarrow (k-8)^2=0$.
Use zero product property.
$\Rightarrow k-8=0$.
Solve for $k$.
$\Rightarrow k=8$.
Hence, the solution is $k=8$.
