We are given the first two terms x^2 - 12x and we need the third term to make it a perfect square trinomial.
A perfect square trinomial results from squaring a binomial. It is in the form:
[tex](x+y)^2=x^2+2xy+y^2[/tex]So to find the third term, we divide the second term by twice the square root of the first term.
Square root of the first term = x
Twice the square root of the first term = 2x
Second term = -12x
[tex]\frac{-12x}{2x}=-6[/tex]Then, we square the answer.
[tex](-6)^2=36[/tex]The third term, then, must be 36.
