If the quadratic is a perfect square, then there has to be a way to write the quadratic as [tex](x - r)^2[/tex], where [tex]r[/tex] is a root of the equation. Expanding it out, we see that
[tex](x - r)^2 = x^2 - 2rx + r^2[/tex]
Now let's compare this form to the one that we were given. Since [tex]r^2[/tex] matches up with [tex]36[/tex], [tex]r[/tex] has to equal either [tex]6[/tex] or [tex]-6[/tex]. So, since [tex]kx[/tex] in the original equation matches up with [tex]-2rx[/tex] in the equation we found, [tex]k = -2r[/tex] and
[tex]\bf k = -12[/tex] or [tex]\bf 12[/tex]
