finding the constant of a perfect squared trinomial

Question

what would the constant in this equation be? My teacher didn't teach us how to do it and I'm confused on how to find the answer

x²+12x+c

Answer 1

When you have an expression of the form

x² + bx + c,

it is a perfect square only if

c = b² / 4

Then

x² + bx + b²/4 = (x + b /2)²

In this problem, b = 12, so

c = 12²/4 = 144/4 = 36

x² + 12x + 36 = (x + 6)²