document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6686>Question 6686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> place the following equations in the standard form of a quadratic equation (ax^2+bx+c=0)\r<BR>\n" );
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document.write( "a.   4/x^2+3/x-10=0\r<BR>\n" );
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document.write( "b.   6+4/x-1=5/x-3\r<BR>\n" );
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document.write( "c.   3.5x+4.6/x=1.2\r<BR>\n" );
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document.write( "please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3667 by </B><A HREF=/tutors/aboutme.mpl?userid=ichudov><B>ichudov(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ichudov><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=ichudov><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll solve this one and you try other ones (same idea)\r<BR>\n" );
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document.write( "a.   4/x^2+3/x-10=0\r<BR>\n" );
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document.write( "use y instead of 1/x.\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ay%5E2%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2%2B3y%2B-10+=+0 ALIGN=MIDDLE  ALT=\"4y%5E2%2B3y%2B-10+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A4%2A-10=169 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A4%2A-10=169\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=169 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2%2B3y%2B-10 ALIGN=MIDDLE  ALT=\"4y%5E2%2B3y%2B-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2%2B3y%2B-10+=+4%28y-1.25%29%2A%28y--2%29 ALIGN=MIDDLE  ALT=\"4y%5E2%2B3y%2B-10+=+4%28y-1.25%29%2A%28y--2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.25, -2.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "so, my solver says y=5/4, -2. That means that x=1/y = 4/5, -1/2. </SPAN>\n" );
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