Question 69885
{{{x^2 - 6x + 9=0}}} Set equation equal to zero
{{{x^2 - 6x = -9}}} Get similar factors to one side, ie all x's to one side
{{{x^2 - 6x + 9 = -9+9}}} Take half of the 2nd coefficient (6) and square it, then add it to both sides (note: when you take half of the 2nd coefficient, it will be part of the perfect square)
{{{x^2 - 6x + 9 = 0}}} You'll be left with this after simplification
{{{(x-3)^2 = 0}}}Factor the polynomial (note if FOILed, (x-3)^2 becomes x^2-6x+9)
Since the answer is in the form (x-b)^2=0 and there is no extra numbers left over, the original polynomial is a perfect square.