SOLUTION: Helping with homework and this one has us stumped, any help is appreciated. The square of a number plus the number is 6. What is the number? Many thanks,

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Question 863016: Helping with homework and this one has us stumped, any help is appreciated.
The square of a number plus the number is 6. What is the number?
Many thanks,
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number
+n%5E2+%2B+n+=+6+
Complete the square
+n%5E2+%2B+n+%2B+%281%2F2%29%5E2+=+6+%2B+%281%2F2%29%5E2+
+n%5E2+%2B+n+%2B+1%2F4+=+6+%2B+1%2F4+
+%28+n+%2B+1%2F2+%29%5E2+=+25%2F4+
+%28+n+%2B+1%2F2+%29%5E2+=+%28+5%2F2+%29%5E2+
Take the square root of both sides
+n+%2B+1%2F2+=+5%2F2+
+n+=+4%2F2+
+n+=+2+
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check answer:
+2%5E2+%2B+2++=+6+
+4+%2B+2+=+6+
+6+=+6+
OK
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A negative number also satisfies the equation
+n+%2B+1%2F2+=+-%285%2F2%29+
+n+=+-%286%2F2%29+
+n+=+-3+
and
+%28-3%29%5E2+%2B+%28-3%29+=+6+
+9+-+3+=+6+
+6+=+6+
OK