ANSWER
The missing constant term is 64
EXPLANATION
The given expression is
[tex] {x}^{2} - 16x[/tex]
Let the k be the constant term, then
[tex] {x}^{2} - 16x + k[/tex]
is a perfect square.
This implies that, the discriminant is zero.
The discriminant is
[tex]D= {b}^{2} - 4ac[/tex]
[tex] {( - 16)}^{2} - 4(1)(k) = 0[/tex]
[tex]256 - 4k = 0[/tex]
[tex] - 4k = - 256[/tex]
[tex]k = \frac{ - 256}{ - 4} [/tex]
[tex]k = 64[/tex]
