document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339346>Question 339346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of 2 consecutive positive integers is 71 more than their sum. Find the integers.\r<BR>\n" );
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document.write( "I have been reviewing my text for a couple of hours now. I cannot figure this one out. Please, please, please help!!!!\r<BR>\n" );
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document.write( "Thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243191 by </B><A HREF=/tutors/aboutme.mpl?userid=Kalmetam><B>Kalmetam(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Kalmetam><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi!  Try to make your own equation, then it'll be easy..\r<BR>\n" );
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document.write( "So two consecutive positive integers?\r<BR>\n" );
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document.write( "Let's say one integer is \"x\" and since they are consecutive, that means the 2nd is x+1.. right? \r<BR>\n" );
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document.write( "So let's try to make an equation:\r<BR>\n" );
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document.write( "The PRODUCT of two consecutive integers.. so that would be\r<BR>\n" );
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document.write( "x(x+1)\r<BR>\n" );
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document.write( "and the second part is 71 more than their sum..<BR>\n" );
document.write( "how can you express that without using other variables?  <BR>\n" );
document.write( "Well, the two numbers are x and x+1 right? and the product is 71 more.. right?\r<BR>\n" );
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document.write( "So you'd get on that side..  71+[x+(x+1)]\r<BR>\n" );
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document.write( "So in the end..  x(x+1)=71+[x+(x+1)]\r<BR>\n" );
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document.write( "Try simplifying the left side:\r<BR>\n" );
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document.write( "x+x^2=71+[x+(x+1)]\r<BR>\n" );
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document.write( "Now simplify the right side:\r<BR>\n" );
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document.write( "x+x^2=72+2x\r<BR>\n" );
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document.write( "Move over that x from the left to the right to simplify it more\r<BR>\n" );
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document.write( "x^2=72+x\r<BR>\n" );
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document.write( "Now square root both sides to cancel out the x^2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%2872%2Bx%29 ALIGN=MIDDLE  ALT=\"x=sqrt%2872%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then if you plot bothsides on a graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-20%2C+20%2C+-15%2C+15%2C+x%2C+sqrt%2872%2Bx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-20%2C+20%2C+-15%2C+15%2C+x%2C+sqrt%2872%2Bx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So apparently, the answer is x=9 (meaning that the second number (x+1) is 10)\r<BR>\n" );
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document.write( "Let's check:\r<BR>\n" );
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document.write( "9*10=90<BR>\n" );
document.write( "9+10=19\r<BR>\n" );
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document.write( "and the product is 71 more than the sum, right?\r<BR>\n" );
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document.write( "90-19=71..\r<BR>\n" );
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document.write( "So our answers must be correct..\r<BR>\n" );
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document.write( "the numbers are 9 and 10   </SPAN>\n" );
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