document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854758>Question 854758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What multiplies to give you -60 and adds to give you -1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514886 by </B><A HREF=/tutors/aboutme.mpl?userid=Seutip><B>Seutip(231)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Seutip><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/cgi-bin/show-face.mpl?user=Seutip><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a - be one of the number<BR>\n" );
document.write( "    b - be the second number\r<BR>\n" );
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document.write( "When given a question of this nature, you can look upon the two numbers as the factors in two polynomials that give you a quadratic when multiplied. That sounds complicated, but I mean this: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+a%29%28x+%2B+b%29+ ALIGN=MIDDLE  ALT=\"%28x+%2B+a%29%28x+%2B+b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use our friend Mr. Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28a+%2B+b%29x+%2B+ab+ ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28a+%2B+b%29x+%2B+ab+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So they give you a product of \"ab\" and a sum of \"a + b\". You are looking for exactly that, two numbers that multiply to give a product you specify and add to give the sum you specify. \r<BR>\n" );
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document.write( "If you substitute the sum, -1, and the product, -60, you get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28-1%29x%2B%28-60%29-0 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28-1%29x%2B%28-60%29-0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-60=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since it's not a perfect trinomial we use completing the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2B1%2F4=60%2B1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=60%2B1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > It's 1/4 because 3rd term = ((-1)/2)^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-1%2F2%29%5E2=sqrt%2860%2A1%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-1%2F2%29%5E2=sqrt%2860%2A1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2=sqrt15 ALIGN=MIDDLE  ALT=\"x-1%2F2=sqrt15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt15%2B1%2F2 ALIGN=MIDDLE  ALT=\"x=sqrt15%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope that helps!\r<BR>\n" );
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