20 Identify the value of c that would make this a perfect square trinomial. x^2-16x+underline ( ) square

To make the quadratic expression \(x^2 - 16x + c\) a perfect square trinomial, we need to find the value of \(c\) that completes the square.<br /><br />A perfect square trinomial takes the form \((x - a)^2 = x^2 - 2ax + a^2\).<br /><br />Comparing this with \(x^2 - 16x + c\), we see that:<br />\[<br />-2a = -16 \implies a = 8<br />\]<br /><br />Now, we need to find \(c\):<br />\[<br />c = a^2 = 8^2 = 64<br />\]<br /><br />Therefore, the value of \(c\) that makes \(x^2 - 16x + c\) a perfect square trinomial is:<br />\[<br />\boxed{64}<br />\]