Expert: Jack Cheng - 11/6/2006

Question
for all values of x

x2 + 6x + 4 = (4 + p)2 + q

find the values of p and q

thanks a lot, mate

Answer
Hi Adam,

By your question, I am assuming you mean:
x^2 + 6x + 4 = (4+p)^2 + q, where the ^2 means squared.

This question basically asks you to "Complete the Square".

Using the completing the square formula:
x^2 + 6x + 4 = 0
x^2 + 6x = -4
x^2 + 6x + 9 -9 = -4     ***
x^2 + 6x + 9 = 5
(x+3)^2 = 5              ***
(x+3)^2 - 5 = 0

So x^2 + 6x +4 = (x+3)^2 - 5. In other words, p=3 and q=-5.

The most important steps of completing the square is starred. The +9 and -9 equaled 0 and add nothing to the equation. I chose 9 because it's (6/2)^2. And because I chose 9, the equation factors easily into (x+3)^2.

See if you can complete the square for this problem:
x^2 + 10x + 10

The answer is (x+5)^2 - 15.

For more information on completing the square:
http://www.sosmath.com/algebra/quadraticeq/complsquare/complsquare.html

I hope this helps,

~ Jack