SOLUTION: twice a number is 8 less than its square. what is the number?

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Question 50015: twice a number is 8 less than its square. what is the number?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the required number(s) be n.
From the problem description, you can write:
2n+=+n%5E2-8 Subtract 2n from both sides.
n%5E2-2n-8+=+0 Solve by factoring.
%28n%2B2%29%28n-4%29+=+0 Apply the zero product principle.
n%2B2+=+0 and/or n-4+=+0
If n%2B2+=+0 then n+=+-2
If n-4+=+0 then n+=+4
There are two solutions to this problem:
n = -2 and
n = 4
Check:
n = -2
2%28-2%29+=+%28-2%29%5E2-8
-4+=+4-8
-4+=+-4
n = 4
2%284%29+=+%284%29%5E2-8
8+=+16-8
8+=+8
Both solutions work.