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Math Help - help finding x-coordinates of points of intersection

  1. #1
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    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.
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  2. #2
    Senior Member vincisonfire's Avatar
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    You can also multiply both side by -1 to get  x^2+2x-15=0
    You must find number such that the product is -15 and the sum is 2.
     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 *\frac{-b\pm\sqrt{b^2-4ac}}{2a}
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