Find the value of c that makes p squared + 18p + c a perfect square

i would like for you to explain it to me, all answers would be appreciated.

81.

Easiest way to find the perfect square. Use the middle one and divide by 2. In this case, 18. 18 divide by 2 is 9. 9^2 is 81

Hi, John!

Remember, that (a + b)² = a² + 2ab + b². So, if "p² + 18p + x," is a perfect square, then:

18p = 2px.

Solving for x,
x = 9.

Set c=x², and we have c = 81, and (p + 9)² = p² + 18p + 81, a perfect square.

Answer:
c = 81