document.write( "Question 291619: Six times a number added to twice the reciprocal of a number equals 13. Find the number(s). \n" ); document.write( "

Algebra.Com's Answer #210838 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"n\"$ = the unknown number
\n" ); document.write( "given:
\n" ); document.write( " $\"6n+%2B+2%2A%281%2Fn%29+=+13\"$
\n" ); document.write( "Multiply both sides by $\"n\"$
\n" ); document.write( " $\"6n%5E2+%2B+2+=+13n\"$
\n" ); document.write( " $\"6n%5E2+-+13n+%2B+2+=+0\"$
\n" ); document.write( "Solve using quadratic formula
\n" ); document.write( " $\"n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+6\"$
\n" ); document.write( " $\"b+=+-13\"$
\n" ); document.write( " $\"c+=+2\"$
\n" ); document.write( " $\"n+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A6%2A2+%29%29%2F%282%2A6%29+\"$
\n" ); document.write( " $\"n+=+%2813+%2B-+sqrt%28169+-+48+%29%29%2F12+\"$
\n" ); document.write( " $\"n+=+%2813+%2B-+sqrt%28121+%29%29%2F12+\"$
\n" ); document.write( " $\"n+=+%2813+%2B-+11%29%2F12\"$
\n" ); document.write( "The solutions are:
\n" ); document.write( " $\"n+=+%2813+%2B+11%29%2F12\"$
\n" ); document.write( " $\"n+=+2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"n+=+%2813+-+11%29%2F12\"$
\n" ); document.write( " $\"n+=+1%2F6\"$
\n" ); document.write( "Both these solutions work if you plug them
\n" ); document.write( "back into $\"6n+%2B+2%2A%281%2Fn%29+=+13\"$
\n" ); document.write( " \n" ); document.write( "

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