SOLUTION: Is the following trinomial a perfect square: x^2 - 6x + 9 I do not understand what method I am to use to figure this out, can anyone help me out please? Thank you

Algebra ->  Equations -> SOLUTION: Is the following trinomial a perfect square: x^2 - 6x + 9 I do not understand what method I am to use to figure this out, can anyone help me out please? Thank you      Log On


   

Question 69885: Is the following trinomial a perfect square:
x^2 - 6x + 9
I do not understand what method I am to use to figure this out, can anyone help me out please? Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+6x+%2B+9=0 Set equation equal to zero
x%5E2+-+6x+=+-9 Get similar factors to one side, ie all x's to one side
x%5E2+-+6x+%2B+9+=+-9%2B9 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%5E2+-+6x+%2B+9+=+0 You'll be left with this after simplification
%28x-3%29%5E2+=+0Factor 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.