document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186422>Question 186422</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,  I am more of an older folk here so its not for homework.  Actually it was a question asked to me and I have had a hard time to figure it out and its driving me nuts.  I also was trying to show someone that there are sites out there for help in which it does not cost you.  I think its wonderful you offer this.  Ok here it goes.  What two numbers when added together equals -6 and what same two numbers when multiplied equals -12.   I hope you can help so I can show my friend there are people out there quite kind like you.  Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139713 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=139713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"two numbers when added together equals -6 \" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=-6 ALIGN=MIDDLE  ALT=\"x%2By=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "\"same two numbers when multiplied equals -12\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=-12 ALIGN=MIDDLE  ALT=\"x%2Ay=-12\"   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%2By=-6 ALIGN=MIDDLE  ALT=\"x%2By=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-6-x ALIGN=MIDDLE  ALT=\"y=-6-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract \"x\" from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-6 ALIGN=MIDDLE  ALT=\"y=-x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ay=-12 ALIGN=MIDDLE  ALT=\"x%2Ay=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%28-x-6%29=-12 ALIGN=MIDDLE  ALT=\"x%2A%28-x-6%29=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-6 ALIGN=MIDDLE  ALT=\"y=-x-6\"   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%2A%28-x%29-x%286%29=-12 ALIGN=MIDDLE  ALT=\"x%2A%28-x%29-x%286%29=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-6x=-12 ALIGN=MIDDLE  ALT=\"-x%5E2-6x=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x=12 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by -1 to make the leading coefficient positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-12=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 12 from both sides.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12 ALIGN=MIDDLE  ALT=\"c=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-12 ALIGN=MIDDLE  ALT=\"c=-12\"   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+%2B-+sqrt%28+36-4%281%29%28-12%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-12%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   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+%2B-+sqrt%28+36--48+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36--48+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28-12%29 ALIGN=MIDDLE  ALT=\"4%281%29%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   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+%2B-+sqrt%28+36%2B48+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36%2B48+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836--48%29 ALIGN=MIDDLE  ALT=\"sqrt%2836--48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2B48%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2B48%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+%2B-+sqrt%28+84+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+84+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   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+%2B-+sqrt%28+84+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+84+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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+%2B-+2%2Asqrt%2821%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+2%2Asqrt%2821%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%2821%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%2821%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3+%2B-+sqrt%2821%29 ALIGN=MIDDLE  ALT=\"x+=+-3+%2B-+sqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2Bsqrt%2821%29 ALIGN=MIDDLE  ALT=\"x+=+-3%2Bsqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3-sqrt%2821%29 ALIGN=MIDDLE  ALT=\"x+=+-3-sqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2Bsqrt%2821%29 ALIGN=MIDDLE  ALT=\"x+=+-3%2Bsqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3-sqrt%2821%29 ALIGN=MIDDLE  ALT=\"x+=+-3-sqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "which approximate to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.583 ALIGN=MIDDLE  ALT=\"x=1.583\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7.583 ALIGN=MIDDLE  ALT=\"x=-7.583\"   DISABLED_style= \"max-width:90%; height:auto;\" > (use a calculator to find the approximate values).\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the numbers are roughly 1.583 and -7.583 (in either order)\r<BR>\n" );
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document.write( "Note:  1.583 + -7.583 = -6 and  1.583 * -7.583 = -12.003889 (which is very close) </SPAN>\n" );
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