document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=861827>Question 861827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If one end of a line whose length is 13 Units is the point (4, 8)<BR>\n" );
document.write( "and the ordinate of the other end is 3. What is its abscissa? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #519389 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=519389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If one end of a line whose length is 13 Units is the point (4, 8)<BR>\n" );
document.write( "and the ordinate of the other end is 3. What is its abscissa?<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Make (4,8) the center of a circle of radius 13<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2+%2B+%28y-8%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2+%2B+%28y-8%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the intersection(s) of x=3 and the circle.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2+%2B+%28y-8%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2+%2B+%28y-8%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-4%29%5E2+%2B+%28y-8%29%5E2+=+169 ALIGN=MIDDLE  ALT=\"%283-4%29%5E2+%2B+%28y-8%29%5E2+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+16y+%2B+65+=+169 ALIGN=MIDDLE  ALT=\"y%5E2+-+16y+%2B+65+=+169\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+16y+-+104+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+16y+-+104+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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%2B-16x%2B-104+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B-104+=+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=%28-16%29%5E2-4%2A1%2A-104=672 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-16%29%5E2-4%2A1%2A-104=672\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=672 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--16%2B-sqrt%28+672+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--16%2B-sqrt%28+672+%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-%28-16%29%2Bsqrt%28+672+%29%29%2F2%5C1+=+20.9614813968157 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+672+%29%29%2F2%5C1+=+20.9614813968157\"   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-%28-16%29-sqrt%28+672+%29%29%2F2%5C1+=+-4.96148139681572 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-16%29-sqrt%28+672+%29%29%2F2%5C1+=+-4.96148139681572\"   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%2B-16x%2B-104 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B-104\"   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%2B-16x%2B-104+=+%28x-20.9614813968157%29%2A%28x--4.96148139681572%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-16x%2B-104+=+%28x-20.9614813968157%29%2A%28x--4.96148139681572%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 20.9614813968157, -4.96148139681572.\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%2B-16%2Ax%2B-104+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B-104+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "==========<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8+%2B-+2sqrt%2842%29 ALIGN=MIDDLE  ALT=\"y+=+8+%2B-+2sqrt%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );