# Thread: I'm not sure what this topic is called?

1. ## I'm not sure what this topic is called?

My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

Heres the question:

given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

Any help appreciated

2. Originally Posted by nickboi
My maths teacher set my some homework which we havent covered yet. I wondered what topic this would be under?

Heres the question:

given that x^2-14x+a=(x+b)^2 for all values of x, find the value of a and the value of b.

Any help appreciated
Hello nickboi,

This exercise has to do with "completing the square". With a quadratic and linear term given, what constant would you have to add in order for that to become a perfect square trinomial. Then, your perfect square trinomial becomes a binomial squared.

3. Thanks for the help. But im not quite sure what you mean by "Then, your perfect square trinomial becomes a binomial squared."

4. Go ahead and multiply out the right side:
$\displaystyle x^2- 14x+ a= x^2+ 2b+ b^2$
In order that those be the same for all x, you must have the same coefficients: -14= 2b and a= b^2.

As masters said, that is basically "completing the square".

5. Thanks you two, i'll give that a try and post my success.

6. It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.

7. Originally Posted by nickboi
It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.
Right back at ya!