Thank you for the opportunity to help you with your question!

To evaluate a quantratic expression we use the quadratic formula below:

We assume the equation looks like this

ax^{2} +bx +c

The value of x is given by:

In our equation b^{2}
+ 6b +9 can alos be written as

x^{2}
+ 6x +9

According to the formula the value of a is 1, the value of b is 6 and the value of c is 9. Please notice that I have replaced b with x to make it easy to understand.

Filling the formula with the values gives

(-6 (+ or -) Square root of ( 6^{2}
- 4(1 *9))/2(1)

Solving the square root part

Square root of (36-36) is 0

Solving Further

-6 (+ or -) 0 all of it divided by 2 gives:

=-3

The value for b in the expression is -3

Notice how easy it was because the square root part gave us a zero.

if you want to know how the quadratic formula is arrived at, please look at the following tutorial:

http://www.purplemath.com/modules/sqrquad2.htm

Please let me know if you need any clarification. I'm always happy to answer your questions.