document.write( "Question 246073: The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. What are the two integers? \n" ); document.write( "
Algebra.Com's Answer #179733 by richwmiller(17219)\"\" \"About 
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let x=first integer and y= second integer
\n" ); document.write( "x=2y+5
\n" ); document.write( "xy=52
\n" ); document.write( "substitute 2y+5 for x in the second equation\r
\n" ); document.write( "\n" ); document.write( "(2y+5)*y=52
\n" ); document.write( "2y^2+5y=52
\n" ); document.write( "divide by 2
\n" ); document.write( "y^2+5/2=26
\n" ); document.write( "we will complete the square
\n" ); document.write( "take (5/2)/2 and square it
\n" ); document.write( "(5/4)^2=25/16
\n" ); document.write( "convert 26 to improper fraction with 16 as the denominator
\n" ); document.write( "y^2+5/2=416/16
\n" ); document.write( "add 25/16 to both sides
\n" ); document.write( "y^2+5/2+25/16=416/16+25/16
\n" ); document.write( "y^2+5/2+25/16=441/16
\n" ); document.write( "factor left hand side
\n" ); document.write( "(y+5/4)^2=441/16\r
\n" ); document.write( "\n" ); document.write( "|y+5/4|=21/4
\n" ); document.write( "y+5/4=-21/4
\n" ); document.write( "y+5/4=21/4
\n" ); document.write( "subtract 5/4 from both sides
\n" ); document.write( "y=-26/4=-13/2
\n" ); document.write( "y=16/4=4
\n" ); document.write( " only 4 is a positive integer
\n" ); document.write( "4*x=52
\n" ); document.write( "x=13
\n" ); document.write( "so the two integers are 4 and 13
\n" ); document.write( "check
\n" ); document.write( "2(4)+5=8+5=13
\n" ); document.write( "ok\r
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