SOLUTION: Find two integers whose sum is 23 and whose product is 90. Show work.

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Question 504028: Find two integers whose sum is 23 and whose product is 90. Show work.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x & y are two integers.
.
x+y = 23
so
y = 23-x
.
x*y = 90
.
substitute y = 23-x
.
x*(23-x) = 90
23 -x^2 = 90
-x^2 +23 -90 = 0
(-x + 5)(x - 18) = 0
.
Check the factoring using FOIL
.
-x^2 +18x +5x -90
OK
.
x = 5 or 18
which means
y = 18 or 5, respectively,
which ensures x+y = 23
.
and we just showed that 5*18 =90
.
So the two integers are 5 and 18.
.
Done.