document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=336529>Question 336529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the following equations for x.<BR>\n" );
document.write( "A)<BR>\n" );
document.write( "(x)(x)/(0.500-x) = 8.30\r<BR>\n" );
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document.write( "B)<BR>\n" );
document.write( "2.94=(2.00 x)2/(0.200-x)\r<BR>\n" );
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document.write( "C)<BR>\n" );
document.write( "x2/0.20+x)(0.030+x) = 2.00\r<BR>\n" );
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document.write( "D)<BR>\n" );
document.write( "4.00x2/(0.100-x)(0.200-x) = 1.45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #241230 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=241230\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x)(x)/(0.500-x) = 8.30<BR>\n" );
document.write( "x^2/(.5-x)=8.3<BR>\n" );
document.write( "x^2=8.3(.5-x)<BR>\n" );
document.write( "x^2=4.15-8.3x<BR>\n" );
document.write( "x^2+8.3x-4.15=0<BR>\n" );
document.write( "x=-8.773..., x=0.4730... (see below)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed <BR>\n" );
document.write( ".<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B8.3x%2B-4.15+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B8.3x%2B-4.15+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%288.3%29%5E2-4%2A1%2A-4.15=85.49 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288.3%29%5E2-4%2A1%2A-4.15=85.49\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=85.49 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+=+%28-8.3%2B-sqrt%28+85.49+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8.3%2B-sqrt%28+85.49+%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=x%5B1%5D+=+%28-%288.3%29%2Bsqrt%28+85.49+%29%29%2F2%5C1+=+0.473040125285524 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%288.3%29%2Bsqrt%28+85.49+%29%29%2F2%5C1+=+0.473040125285524\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%288.3%29-sqrt%28+85.49+%29%29%2F2%5C1+=+-8.77304012528553 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%288.3%29-sqrt%28+85.49+%29%29%2F2%5C1+=+-8.77304012528553\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B8.3x%2B-4.15 ALIGN=MIDDLE  ALT=\"1x%5E2%2B8.3x%2B-4.15\"   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=1x%5E2%2B8.3x%2B-4.15+=+1%28x-0.473040125285524%29%2A%28x--8.77304012528553%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B8.3x%2B-4.15+=+1%28x-0.473040125285524%29%2A%28x--8.77304012528553%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.473040125285524, -8.77304012528553.\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+1%2Ax%5E2%2B8.3%2Ax%2B-4.15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8.3%2Ax%2B-4.15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );