# completing the square

• Sep 18th 2009, 02:29 PM
frozenflames
completing the square
by completing the square the expression that is x^2+14 x +156 equals (x+A)^2+B

so the question is what would A and B equal

this is my last question...i am stumped on a few of these..
• Sep 18th 2009, 03:22 PM
redsoxfan325
Quote:

Originally Posted by frozenflames
by completing the square the expression that is x^2+14 x +156 equals (x+A)^2+B

this is my last question...i am stumped on a few of these..

I'll put you out of you're misery. Given an equation $\displaystyle x^2+bx+c$, You want to get something of the form $\displaystyle x^2+bx+\left(\frac{b}{2}\right)^2+k$, for some constant $\displaystyle k$. (Note that $\displaystyle k+\left(\frac{b}{2}\right)^2=c$.) When factored, this will become $\displaystyle \left(x+\frac{b}{2}\right)^2+k$.

So in this case,$\displaystyle \frac{b}{2}=7$ so $\displaystyle \left(\frac{b}{2}\right)^2=49$.

Break up the equation: $\displaystyle x^2+14x+156=x^2+14x+49+107$

Factor and you're done: $\displaystyle x^2+14x+49+107=(x+7)^2+107$.

So $\displaystyle A=7$ and $\displaystyle B=107$.

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EDIT: You've already figured it out I see. Well, at least you have something to check it against now.
• Sep 18th 2009, 03:28 PM
frozenflames
thanks a lot, but i figured that one out.