SOLUTION: Find two numbers that add to 3 and multiply to -40. (Enter the two numbers separated by a semicolon.) Thanks

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Question 985971: Find two numbers that add to 3 and multiply to -40.
(Enter the two numbers separated by a semicolon.)
Thanks
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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You need to find two integers  x  and  y  from the system of two equations in two unknowns

system%28x+%2B+y+=+3%2C%0D%0Ax%2Ay+=+-40%29.

Express  y  from the first equation  y = 3 - x  and substitute it to the second equation.  You will get

x*(3 - x) = -40.

Solve it:

-x%5E2 + 3x + 40 = 0,

x%5E2 - 3x - 40 = 0,

The roots are  x = 8  and  x = -5   (use the quadratic formula).

From the first equation,  if  x = 8  then  y = -5.
Similarly,  if  x = -5,  then  y = 8.

Answer.  The pairs  (8,-5)  and  (-5,8)  are the solutions.