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

• Jan 9th 2009, 09:54 AM
nickboi
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
• Jan 9th 2009, 10:04 AM
masters
Quote:

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.
• Jan 9th 2009, 10:08 AM
nickboi
Thanks for the help. But im not quite sure what you mean by "Then, your perfect square trinomial becomes a binomial squared."
• Jan 9th 2009, 10:11 AM
HallsofIvy
Go ahead and multiply out the right side:
$x^2- 14x+ a= x^2+ 2b+ b^2$
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".
• Jan 9th 2009, 10:19 AM
nickboi
Thanks you two, i'll give that a try and post my success.
• Jan 9th 2009, 10:24 AM
nickboi
It worked. Thanks a lot. I can now complete the square! I gave both of you thanks.
• Jan 9th 2009, 10:35 AM
masters
Quote:

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!