How do you factor x^2 + 8x - 209 = 0?

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  • Anonymous
    7 years ago
    Favorite Answer

    209 = 19 * 11

    So ---> x² + 8x - 209 = 0

    x² + 19x - 11x - 209 = 0

    x(x + 19) - 11(x + 19) = 0

    (x - 11)(x + 19) = 0

    x = 11 and x = -19

  • 7 years ago

    So....

    Two ways I immediately think of are either using the quadratic formula to find the roots if your supposed to be using that:

    http://www.purplemath.com/modules/quadform.htm

    Or solving by thought process..

    In general in maths a good approach is to generate a fast, rough answer (which is useful for a quick check later) then pad it out with the right numbers.

    So for this question think carefully about what components you know are going to be there....

    For example...

    (X + ? ) ( X - ?)

    You know it must take this form as there is the X^2 and the +/- must be there as there is a negative number ( -209)

    Next you need to start thinking what two numbers multiplied together make 209?

    Also these two numbers must be 8 apart from each other because joining them makes 8.

    A good place to start (the rough answer as mentioned) is often the square root of the number (209) which in this case is 14.46.

    So we know the two numbers you are looking for are around the size of 14 and are 8 apart ,for instance how about 10 and 18 - these numbers are 4 each side of 14, but 10x18=180 not 209, so they are close but not large enough....

    OK I now see others have answered it anyway but I hope my answer helps you learn how to solve it.

    As you can see my example of 10 and 18 was to small so you would try one step up (11 and 19) which is the answer!

  • x^2 + 8x = 209

    x^2 + 8x + 16 = 209 + 16

    (x + 4)^2 = 225

    x + 4 = -15 , 15

    x = -4 - 15 , -4 + 15

    x = -19 , 11

    (x - 11) * (x - (-19)) =>

    (x - 11) * (x + 19)

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