document.write( "Question 517039: The sum of a number and 21 times it's reciprocal is -10. Find the number? \n" ); document.write( "

Algebra.Com's Answer #344609 by josmiceli(19441) $\"\"$ $\"About$

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$\"+n+%2B+21%2A%281%2Fn%29+=+-10+\"$
\n" ); document.write( "Multiply both sides by $\"n\"$
\n" ); document.write( " $\"+n%5E2+%2B+21+=+-10n+\"$
\n" ); document.write( " $\"+n%5E2+%2B+10n+=+-21+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+n%5E2+%2B+10n+%2B+%2810%2F2%29%5E2+=+-21+%2B+%2810%2F2%29%5E2+\"$
\n" ); document.write( " $\"+n%5E2+%2B+10n+%2B+25+=+-21+%2B+25+\"$
\n" ); document.write( " $\"+%28+n+%2B+5+%29%5E2+=+4+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+n+%2B+5+=+2+\"$
\n" ); document.write( " $\"+n+=+-3+\"$
\n" ); document.write( "and also
\n" ); document.write( " $\"+n+%2B+5+=+-2+\"$
\n" ); document.write( " $\"+n+=+-7+\"$
\n" ); document.write( "check answers:
\n" ); document.write( " $\"+n+%2B+21%2A%281%2Fn%29+=+-10+\"$
\n" ); document.write( " $\"+-3+%2B+21%2A%281%2F%28-3%29%29+=+-10+\"$
\n" ); document.write( " $\"+-3+-+7+=+-10+\"$
\n" ); document.write( " $\"+-10+=+-10+\"$
\n" ); document.write( "OK
\n" ); document.write( " $\"+-7+%2B+21%2A%281%2F%28-7%29%29+=+-10+\"$
\n" ); document.write( " $\"+-7+-+3+=+-10+\"$
\n" ); document.write( " $\"+-10+=+-10+\"$ \n" ); document.write( "

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