document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465444>Question 465444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you create a quadratic equation if you only have the solutions? I am really not getting the quadratic equation math at all. Example if I have theses two numbers, 8 and 4/5 as solutions to create a quadratice equation.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318973 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318973\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation is one in which the<BR>\n" );
document.write( "highest power of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This will automatically happen when you <BR>\n" );
document.write( "multiply something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+2%29%2A%28x+-7%29+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+2%29%2A%28x+-7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+5x+-+14+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+5x+-+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Now suppose you have 2 solutions to a <BR>\n" );
document.write( "quadratic equation, <BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+8+ ALIGN=MIDDLE  ALT=\"+x+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4%2F5+ ALIGN=MIDDLE  ALT=\"+x+=+4%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+8+=+0+ ALIGN=MIDDLE  ALT=\"+x+-+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F5 ALIGN=MIDDLE  ALT=\"+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+4%2F5+=+0+ ALIGN=MIDDLE  ALT=\"+x+-+4%2F5+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The key now is that if you multiply (1) and (2),<BR>\n" );
document.write( "you will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%2A0+=+0 ALIGN=MIDDLE  ALT=\"+0%2A0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-8%29%2A%28x-4%2F5%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x-8%29%2A%28x-4%2F5%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now do the multiplication<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+8x+-+%284%2F5%29%2Ax+%2B+32%2F5+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+8x+-+%284%2F5%29%2Ax+%2B+32%2F5+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%5E2+-+40x+-+4x+%2B+32+=+0+ ALIGN=MIDDLE  ALT=\"+5x%5E2+-+40x+-+4x+%2B+32+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%5E2+-+44x+%2B+32+=+0+ ALIGN=MIDDLE  ALT=\"+5x%5E2+-+44x+%2B+32+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Now you can check the answer<BR>\n" );
document.write( "Does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4%2F5+ ALIGN=MIDDLE  ALT=\"+x+=+4%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > work?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A%284%2F5%29%5E2+-+44%2A%284%2F5%29+%2B+32+=+0+ ALIGN=MIDDLE  ALT=\"+5%2A%284%2F5%29%5E2+-+44%2A%284%2F5%29+%2B+32+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A%2816%2F25%29+-+44%2A%2820%2F25%29+%2B+32+=+0+ ALIGN=MIDDLE  ALT=\"+5%2A%2816%2F25%29+-+44%2A%2820%2F25%29+%2B+32+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25+ ALIGN=MIDDLE  ALT=\"+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80+-+880+%2B+800+=+0+ ALIGN=MIDDLE  ALT=\"+80+-+880+%2B+800+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+880+-+880+=+0+ ALIGN=MIDDLE  ALT=\"+880+-+880+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "You can check the other solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );