SOLUTION: if a number is added to twice its square, the result is 6. find the number.

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Question 216313: if a number is added to twice its square, the result is 6. find the number.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = the number, then:
n%2B2n%5E2+=+6 Subtract 6 from both sides.
2n%5E2%2Bn-6+=+0 Factor.
%282n-3%29%28n%2B2%29+=+0 Apply the zero product rule.
2n-3+=+0 or n%2B2+=+0 which means that...
highlight%28n+=+3%2F2%29 or highlight%28n+=+-2%29
Check:
%283%2F2%29%2B2%283%2F2%29%5E2+=+%283%2F2%29%2B2%289%2F4%29=%283%2F2%29%2B%289%2F2%29+=+12%2F2=6
%28-2%29%2B2%28-2%29%5E2+=+%28-2%29%2B2%284%29 = -2%2B8+=+6