document.write( "Question 37297This question is from textbook Intermediate Algebra
\n" ); document.write( ": the question is the sum of a number and 6 times it's receiprocal is -5. How do I solve this? \n" ); document.write( "
Algebra.Com's Answer #22962 by jcmtnez(53)\"\" \"About 
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Given a number x, the reciprocal of x is 1/x.\r
\n" ); document.write( "\n" ); document.write( "6 times the reciprocal of x, is 6/x
\n" ); document.write( "and the problem says that the sum of x and its reciprocal is equal to -5,then:\r
\n" ); document.write( "\n" ); document.write( "x+6/x=-5 Now we have to eliminate the denominator by multiplying the entire expression by x\r
\n" ); document.write( "\n" ); document.write( "x(x)+x(6/x)=x(-5)
\n" ); document.write( "x^2+6=-5x
\n" ); document.write( "x^2+5x+6=0 Now we have to solve the equation to solve the problem and find the solutions.\r
\n" ); document.write( "\n" ); document.write( "The solution is given using the general formula for quadratic equations:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r
\n" ); document.write( "\n" ); document.write( "Solutions: x1=-2,x2=-3
\n" ); document.write( "We have to solutions and therefore two pair of number for which the stated condition hold.
\n" ); document.write( "Those numbers are:
\n" ); document.write( "-2 and -1/2 , -3 and -1/3\r
\n" ); document.write( "\n" ); document.write( "Proof:\r
\n" ); document.write( "\n" ); document.write( "-2+6(-1/2) = -2-3=-5
\n" ); document.write( "-3+6(-1/3) = -3-2=-5\r
\n" ); document.write( "\n" ); document.write( "Then the solutions are true.
\n" ); document.write( "Any doubt?:) \r
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