document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158321>Question 1158321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what numbers multiply to -9 and add to 5<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781238 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=781238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = one of the numbers and y = the other of the numbers.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "x + y =  5<BR>\n" );
document.write( "x * y = -9<BR>\n" );
document.write( "solve for y in the first equation to get y = 5 - x<BR>\n" );
document.write( "replace y with 5 - x in the second equation to get x * (5 - x) = -9<BR>\n" );
document.write( "simplify to get 5x - x^2 = -9<BR>\n" );
document.write( "subtract the left side of the equation from both sides of the equation to get:<BR>\n" );
document.write( "5x - x^2 - (5x - x^2) = -9 - (5x - x^2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "5x - x^2 - 5x + x^2 = 9 - 5x + x^2<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "0 = 9 - 5x + x^2<BR>\n" );
document.write( "reorder the terms in descending order of degree to get:<BR>\n" );
document.write( "0 = x^2 - 5x - 9<BR>\n" );
document.write( "switch sides to get:<BR>\n" );
document.write( "x^2 - 5x - 9 = 0<BR>\n" );
document.write( "solve this quadratic equation using the quadratic formula to get:<BR>\n" );
document.write( "x = (-5 + sqrt(61)) / 2 or x = (-5 - sqrt(61)) / 2<BR>\n" );
document.write( "use your calculator to find the decimal equivalent of these values to get:<BR>\n" );
document.write( "x = 1.405124838 or x = -6.405124838<BR>\n" );
document.write( "replace x with 1.405124838 in the first equation to get:<BR>\n" );
document.write( "1.405124838 + y = 5<BR>\n" );
document.write( "solve for y to get y = -6.405124838<BR>\n" );
document.write( "replace x and y with these values in the second equation to get:<BR>\n" );
document.write( "x * y = 1.405124838 * -6.405124838 = -9<BR>\n" );
document.write( "the values are confirmed to be good.<BR>\n" );
document.write( "your solution is that one of the numbers is 1.405124838 and the other number is -6.405124838.<BR>\n" );
document.write( "the numbers shown are rounded by the calculator to 9 decimal digits.<BR>\n" );
document.write( "the actual values have more decimal digits than that.<BR>\n" );
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