SOLUTION: What adds to give you '+90' and multiplies to give you '-7200'?

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Question 340042: What adds to give you '+90' and multiplies to give you '-7200'?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
What adds to give you '+90' and multiplies to give you '-7200'?

Let the two numbers be x and y

Then 

x + y = 90
   xy = -7200

Solve the first for y:

y = 90 - x

Substitute in the other equation:

  x(90 - x) = -7200

  90x - x² = -7200

-x² + 90x + 7200 = 0

 x² - 90x - 7200 = 0

Solve by the quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+



x+=+%2890+%2B-+sqrt%288100%2B28800+%29%29%2F2+

x+=+%2890+%2B-+sqrt%2836900+%29%29%2F2+

x+=+%2890+%2B-+sqrt%2836900+%29%29%2F2+

x+=+%2890+%2B-+sqrt%28900%2A41+%29%29%2F2+

x+=+%2890+%2B-+30sqrt%2841+%29%29%2F2+

x+=+%28+30%283+%2B-+sqrt%2841%29%29+%29%2F2+

  15
x+=+%28cross%2830%29%283+%2B-+sqrt%2841%29%29%29%2Fcross%282%29+

x+=+15%283+%2B-+sqrt%2841%29%29+

Since the equations 

x + y = 90
   xy = -7200

are symmetrical in x (the same if x and y are interchanged)

the two solutions are the values of x and y

So the answers are

15%283+%2B+sqrt%2841%29%29+ and 15%283+-+sqrt%2841%29%29+ 

-------------------------

Checking to see if they add to +90

15%283+%2B+sqrt%2841%29%29+%2B15%283+-+sqrt%2841%29%29+
45+%2B+15sqrt%2841%29+%2B45+-+15sqrt%2841%29%29+
90

Checking to see if they multiply to give -7200

15%283+%2B+sqrt%2841%29%29%2A15%283+-+sqrt%2841%29%29+
225%283+%2B+sqrt%2841%29%29%283+-+sqrt%2841%29%29+
225%289-3sqrt%2841%29%2B3sqrt%2841%29+-+41%29+
225%289-cross%283sqrt%2841%29%29%2Bcross%283sqrt%2841%29%29+-+41%29+
225%289-41%29+
225%28-32%29+
-7200

So those are the right answers.

Edwin