SOLUTION: A pleasant day Sir or Madam. please help me with this word problem involving rational expressions. If twice the reciprocal is subtracted from the number, the result is -7/5. F

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A pleasant day Sir or Madam. please help me with this word problem involving rational expressions. If twice the reciprocal is subtracted from the number, the result is -7/5. F      Log On


   

Question 683656: A pleasant day Sir or Madam. please help me with this word problem involving rational expressions.
If twice the reciprocal is subtracted from the number, the result is -7/5. Find the number.
Thank you very much for your help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the unknown number = +n+
given:
+n+-+2%2A%281%2Fn%29+=+-7%2F5+
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Multiply both sides by +5n+
+5n%5E2+-+10+=+-7n+
+5n%5E2+%2B+7n+-+10+=+0+
Use the quadratic formula
+n+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+7+
+c+=+-10+
+n+=+%28-7+%2B-+sqrt%28+7%5E2+-+4%2A5%2A%28-10%29+%29%29+%2F+%282%2A5%29+
+n+=+%28-7+%2B-+sqrt%28+49+%2B+200+%29%29+%2F+10+
+n+=+%28-7+%2B-+sqrt%28+249+%29%29+%2F+10+
The 2 answers are
+n+=++%28-7+%2B+sqrt%28+249+%29%29+%2F+10+
+n+=++%28-7+-+sqrt%28+249+%29%29+%2F+10+
I could have made a mistake. You might want
to get a 2nd opinion on this.