document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209239>Question 1209239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what number multiplies to get -432 and adds to get 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847893 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=847893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x is one of the unknown numbers<BR>\n" );
document.write( "6-x must be the other number so the items add to 6.<BR>\n" );
document.write( "x + (6-x) = 6\r<BR>\n" );
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document.write( "Multiplying the values and setting the product equal to -432, will give:<BR>\n" );
document.write( "x*(6-x) = -432<BR>\n" );
document.write( "6x-x^2 = -432<BR>\n" );
document.write( "6x-x^2+432 = 0<BR>\n" );
document.write( "-x^2+6x+432 = 0\r<BR>\n" );
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document.write( "You could use trial-and-error to factor. But this method could be a bit slow and the quadratic formula is the much more efficient route.\r<BR>\n" );
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document.write( "Compare -x^2+6x+432 = 0 with the template ax^2+bx+c = 0<BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = 432<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6%2B-++42%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6%2B-++42%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6%2B42%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6%2B42%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6-42%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6-42%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-18 ALIGN=MIDDLE  ALT=\"x+=+-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24 ALIGN=MIDDLE  ALT=\"x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your quadratic formula scratch work doesn't have to be as detailed. \r<BR>\n" );
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document.write( "If x = <font color=red>-18</font> is one of the numbers, then 6-x = 6-(-18) = 6+18 = <font color=red>24</font> is the other number.\r<BR>\n" );
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document.write( "If x = <font color=red>24</font>, then 6-x = 6-24 = <font color=red>-18</font>\r<BR>\n" );
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document.write( "Therefore <font color=red>the pair of values are <u>-18 and 24</u></font>\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "-18*24 = -432<BR>\n" );
document.write( "-18+24 = 6<BR>\n" );
document.write( "Both requirements are confirmed.<BR>\n" );
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