document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=998411>Question 998411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What adds to give you -35 but multiplies to give you -3800? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616187 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=616187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a is one of the numbers<BR>\n" );
document.write( "b is the other number<BR>\n" );
document.write( "a + b = -35<BR>\n" );
document.write( "a * b = -3800<BR>\n" );
document.write( "from the first equation, solve for b in terms of a to get b = -a - 35<BR>\n" );
document.write( "in the second equation, replace b with -a - 35 to get:<BR>\n" );
document.write( "a * (-a - 35) = -3800<BR>\n" );
document.write( "remove parentheses to get:<BR>\n" );
document.write( "-a^2 - 35a = -3800<BR>\n" );
document.write( "add 3800 to both sides of this equation to get:<BR>\n" );
document.write( "-a^2 - 35a + 3800 = 0<BR>\n" );
document.write( "multiply both sides of this equation by -1 to get:<BR>\n" );
document.write( "a^2 + 35a - 3800 = 0<BR>\n" );
document.write( "this is a quadratic equation that can be factored to get:<BR>\n" );
document.write( "a1 = 46.58002809<BR>\n" );
document.write( "a2 = -81.58002809\r<BR>\n" );
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document.write( "you know that:\r<BR>\n" );
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document.write( "a1 + b1 = -35<BR>\n" );
document.write( "a2 + b2 = -35\r<BR>\n" );
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document.write( "solve for b1 and b2 to get:\r<BR>\n" );
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document.write( "b1 = -81.58002809<BR>\n" );
document.write( "b2 = 46.58002809\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "a1 = 46.58002809 and b1 = -81.58002809<BR>\n" );
document.write( "a2 = -81.58002809 and b2 = 46.58002809\r<BR>\n" );
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document.write( "what this says is:\r<BR>\n" );
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document.write( "if a = 46.58..., then b = -81.58...<BR>\n" );
document.write( "if a = -81.58..., then b = 46.58...\r<BR>\n" );
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document.write( "these equaations satisfy the two equations we started with simultaneously.\r<BR>\n" );
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document.write( "those equations are:\r<BR>\n" );
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document.write( "a + b = -35<BR>\n" );
document.write( "a * b = -3800\r<BR>\n" );
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document.write( "we can graph these equations and we can then see the solution graphically.\r<BR>\n" );
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document.write( "let x = a and y = b,\r<BR>\n" );
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document.write( "you get x + y = -35<BR>\n" );
document.write( "x * y = -3800\r<BR>\n" );
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document.write( "solve for y in both equations to get:\r<BR>\n" );
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document.write( "y = -35 - x<BR>\n" );
document.write( "y = -3800 / x\r<BR>\n" );
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document.write( "the intersections of the graph of these equations is our solution because that point is common to both equations.\r<BR>\n" );
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document.write( "the graph look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/102202.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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