SOLUTION: how do you use the quadratic formula?

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Question 336454: how do you use the quadratic formula?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
how do you use the quadratic formula?

You first get the equation in this form with the red%28A%29 positive:

red%28A%29x%5E2+%2B+blue%28B%29x+%2B+green%28C%29+=+0

then you substitute in this

 

Then you simplify and you get two answers, one using the + and
one using the -.

Example:

-blue%289%29x+-red%283%29x%5E2+=+green%282%29

Write it in descending order on the left with only 0 on the right:

-red%283%29x%5E2+-+blue%289%29x+-+green%282%29+=+0

Multiply through by -1 to make the first term red%28A%29 positive:

red%283%29x%5E2+%2B+blue%289%29x+%2B+green%282%29+=+0



Now simplify:

x+=+%28-9+%2B-+sqrt%289%5E2-4%2A3%2A2%29+%29%2F6+

x+=+%28-9+%2B-+sqrt%2881-24%29+%29%2F6+

x+=+%28-9+%2B-+sqrt%2857%29+%29%2F6+

The two solutions are:

x+=+%28-9+%2B+sqrt%2857%29+%29%2F6+ and x+=+%28-9+-+sqrt%2857%29+%29%2F6+

You can get the approximate decimal values with a calculator:

x+=+-.2416942608+  and x+=+-2.758305739+

Edwin