1. ## Completing The Square

I was wondering if anyone could help? I was looking over some notes about completing the square, and can anyone tell me why this is true?
x^2+5x+3 =
(x+5/2)^2-(5/2)^2+3

I get the first part, (x+5/2)^2 because this makes up a complete square, but why is there a constant that is taken away?
Thanks alot

2. (5/2)^2 is taken away because it is added in the (x +5/2)^2

You see, the incomplete square is (x^2 +5x).
To make that a perfect square, the square must be completed.
x^2 +5x +(5/2)^2
= (x +5/2)^2

So the (5/2)^2 was added to "complete the square".
Then,
(x +5/2)^2 +3
is not the same anymore as x^2 +5x +3 ----the original expression.
Because
(x +5/2)^2 +3
= x^2 +5x +(5/2)^2 +3.
There is a (5/2)^2 that was added.

So to maintain or to make the value of the new expression to equal the value of the original expression, another (5/2)^2 must be taken away from the new expression.
Hence,
x^2 +5x +3 = (x +5/2)^2 -(5/2)^2 +3

3. Good stuff, as iwent through it step by step i understood where i went wrong now..thanks alot