SOLUTION: two integers have a difference if -30. when the larger integer is increased by 3 and added to the square of the smaller integer, the sum is 189. what are the two integers

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Question 1083623: two integers have a difference if -30. when the larger integer is increased by 3 and added to the square of the smaller integer, the sum is 189. what are the two integers

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+-+y+=+-30+
+y+ must be the larger integer
+y+%2B+3+%2B+x%5E2+=+189+
--------------------------
+-y+=+-x+-+30+
+y+=+x+%2B+30+
-------------------
By substitution:
+x+%2B+30+%2B+3+%2B+x%5E2+=+189+
+x%5E2+%2B+x+-+189+%2B+33+=+0+
+x%5E2+%2B+x+-+156+=+0+
By looking at this, I see:
+%28+x+%2B+13+%29%2A%28+x+-+12+%29+=+0+
------------------------------
If I say +x+=+12+, then
+y+=+x+%2B+30+
+y+=+42+
The integers are 12 and 42
---------------------------
check answers:
+x+-+y+=+-30+
+12+-+42+=+-30+
+-30+=+-30+
OK
and
+y+%2B+3+%2B+x%5E2+=+189+
+42+%2B+3+%2B+12%5E2+=+189+
+45+%2B+144+=+189+
+189+=+189+
OK