Question 274509: I can't find two numbers that multiplied give me negative 270 and added give me negative 49
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's list all of the factors of  (the product needed).
Factors of :
1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
-1,-2,-3,-5,-6,-9,-10,-15,-18,-27,-30,-45,-54,-90,-135,-270
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-270) = -270
2*(-135) = -270
3*(-90) = -270
5*(-54) = -270
6*(-45) = -270
9*(-30) = -270
10*(-27) = -270
15*(-18) = -270
(-1)*(270) = -270
(-2)*(135) = -270
(-3)*(90) = -270
(-5)*(54) = -270
(-6)*(45) = -270
(-9)*(30) = -270
(-10)*(27) = -270
(-15)*(18) = -270
Now let's add up each pair of factors to see if one pair adds to  :
| First Number | Second Number | Sum | | 1 | -270 | 1+(-270)=-269 | | 2 | -135 | 2+(-135)=-133 | | 3 | -90 | 3+(-90)=-87 | | 5 | -54 | 5+(-54)=-49 | | 6 | -45 | 6+(-45)=-39 | | 9 | -30 | 9+(-30)=-21 | | 10 | -27 | 10+(-27)=-17 | | 15 | -18 | 15+(-18)=-3 | | -1 | 270 | -1+270=269 | | -2 | 135 | -2+135=133 | | -3 | 90 | -3+90=87 | | -5 | 54 | -5+54=49 | | -6 | 45 | -6+45=39 | | -9 | 30 | -9+30=21 | | -10 | 27 | -10+27=17 | | -15 | 18 | -15+18=3 |
From the table, we can see that the two numbers  and  add to . Since each pair multiplies to -270, this means that 5 and -54 also multiply to -270.
So the two numbers 5 and -54 both add to -49 and multiply to -270.
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