SOLUTION: Factor: n^2+n-56

Algebra ->  Test -> SOLUTION: Factor: n^2+n-56      Log On


   

Question 731262: Factor:
n^2+n-56
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
n^2+n-56
-------------
find a pair of factors of 56 that differ by 1.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+n%5E2+%2B+n+-+56+
You can try to complete the square
first set the equation equal to zero
+n%5E2+%2B+n+-+56+=+0+
Subtract +56+ from both sides
+n%5E2+%2B+n++=+56+
Take 1/2 of the co-efficient of +x+
square it and add it to both sides
+n%5E2+%2B+n++%2B+%281%2F2%29%5E2+=+%281%2F2%29%5E2+%2B+56+
+n%5E2+%2B+n++%2B+1%2F4+=+1%2F4+%2B+224%2F4+
+n%5E2+%2B+n++%2B+1%2F4+=+225%2F4+
+%28+n+%2B+1%2F2+%29%5E2+=+%2815%2F2%29%5E2+
Take the square root of both sides
+n+%2B+1%2F2+=+15%2F2+
+n+-+14%2F2++=+0+
+n+-+7+=+0+
-------------
also,
+n+%2B+1%2F2+=+-15%2F2+
+n+%2B+16%2F2++=+0+
+n+%2B+8+=+0+
-------------
+%28+n-7+%29%2A%28+n%2B8+%29+=+0+
+n%5E2+%2B+n+-+56++=+%28+n-7+%29%2A%28+n%2B8+%29+