# Thread: help finding x-coordinates of points of intersection

1. ## help finding x-coordinates of points of intersection

I need help with the following problem:

Let S be the region bounded between f(x)=16-x^2 and g(x)=2x+1
Find the x-coordinates of the points of intersection.

I am getting stuck on one step of this problem and am not really sure what to do next. I know that you should begin by setting the two equations equal to each other:

16-x^2=2x+1
-x^2-2x+15=0

When I get to the second step of this problem, I am not really sure what to do next. My calculus book starts to factor in this step, but this problem doesn't look like it can be factored. I am not really sure what I am supposed to do next. If anyone could explain to me how to go about getting the answer to this problem, I would greatly appreciate it. Thanks in advance to anyone who can help me.

2. You can also multiply both side by -1 to get $\displaystyle x^2+2x-15=0$
You must find number such that the product is -15 and the sum is 2.
$\displaystyle x^2+2x-15=(x+a)(x+b)=x^2+(a+b)x+ab$ that's why.
Answer is a=5 and b=-3. There is no trick you have to get a feel for these thing.
You can also use the formula to find root of quadratic equation $\displaystyle *\frac{-b\pm\sqrt{b^2-4ac}}{2a}$