document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476080>Question 476080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two numbers that have a product of -840 and the sum is -22. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326945 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=326945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the two numbers be x and y.<BR>\n" );
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document.write( "The product of the two numbers is -840. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay+=+-840 ALIGN=MIDDLE  ALT=\"x%2Ay+=+-840\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <---- first equation<BR>\n" );
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document.write( "The sum of the two numbers is -22. In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+-22 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+-22\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <---- second equation<BR>\n" );
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document.write( "In the second equation solve for one of the variables in terms of the other. For example solve for x by subtracting y from both sides of the equation. When you do this subtraction you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-y+-+22 ALIGN=MIDDLE  ALT=\"x+=+-y+-+22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute the right side of this equation for x in the first equation.  This substitution leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-y-22%29%2Ay+=+-840 ALIGN=MIDDLE  ALT=\"%28-y-22%29%2Ay+=+-840\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply out the left side by multiplying y times each of the two terms in parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5E2+-22y+=+-+840 ALIGN=MIDDLE  ALT=\"-y%5E2+-22y+=+-+840\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "add 840 to both sides of this equation and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5E2+-22y+%2B+840+=+0 ALIGN=MIDDLE  ALT=\"-y%5E2+-22y+%2B+840+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To get this into standard quadratic form, multiply both sides (all terms) by -1 and the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2B+22y+-+840+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+%2B+22y+-+840+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can solve this by using the quadratic formula, or you can factor it. The left side factors as shown:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+42%29%2A%28y+-20%29+=+0%0D%0A.%0D%0ATo+make+this+equation+equal+to+zero+either+factor+can+be+equal+to+zero.+This+means+that+either%3A%0D%0A.%0D%0A%7B%7B%7By+%2B+42+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > in which case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-42 ALIGN=MIDDLE  ALT=\"y+=+-42\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+20+=+0 ALIGN=MIDDLE  ALT=\"y+-+20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in which case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2B20 ALIGN=MIDDLE  ALT=\"y+=+%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since you now know possible solutions for y, you can return to the second equation and solve for x. Using the second equation, substitute y = -42 and you get for x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%28-42%29+=+-22 ALIGN=MIDDLE  ALT=\"x+%2B+%28-42%29+=+-22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add +42 to both sides and this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+42-22 ALIGN=MIDDLE  ALT=\"x+=+42-22\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So one possible solution to this problem is x = 20 and y = -42<BR>\n" );
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document.write( "Another possible solution occurs when y = +20. You can work this out by solving for x, but you will find that the answer for x is x = -42.<BR>\n" );
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document.write( "The answer now becomes apparent. One of the two numbers is -42 and the other is +20. (Either x = 20 and y = -42 or y = 20 and x = -42).<BR>\n" );
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document.write( "Hope this helps you to understand the process for solving this problem.   </SPAN>\n" );
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