What is the value of #c# in #x^2 + 8x + c# that would make it a perfect-square trinomial?

1 Answer
Jul 27, 2016

If #c = 16#, then #x^2 +8x +16 =(x + 4)^2#

Explanation:

This is the process called "completing the square".

If #x^2 + bx + c# is a perfect square, then there is always the same relation ship between #b and c#

"Find half of #b# and square it" , so #c = (b/2)^2#

#x^2 +8x + (8/2)^2#

=#x^2 + 8x +4^2 = x^2+ 8x +16#

=#(x +4)^2#