document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815416>Question 815416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3x-4y=25<BR>\n" );
document.write( "X^2-y^2=25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490952 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=490952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x-4y=25<BR>\n" );
document.write( "X^2-y^2=25<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "3x-4y=25<BR>\n" );
document.write( "y = (3x-25)/4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "X^2-y^2=25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28%283x-25%29%2F4%29%5E2=25 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28%283x-25%29%2F4%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+-+9x%5E2+%2B+150x+-+625+=+400 ALIGN=MIDDLE  ALT=\"16x%5E2+-+9x%5E2+%2B+150x+-+625+=+400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2+%2B+150x+-+1025+=+0 ALIGN=MIDDLE  ALT=\"7x%5E2+%2B+150x+-+1025+=+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=7x%5E2%2B150x%2B-1025+=+0 ALIGN=MIDDLE  ALT=\"7x%5E2%2B150x%2B-1025+=+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=%28150%29%5E2-4%2A7%2A-1025=51200 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28150%29%5E2-4%2A7%2A-1025=51200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=51200 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+=+%28-150%2B-sqrt%28+51200+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-150%2B-sqrt%28+51200+%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-%28150%29%2Bsqrt%28+51200+%29%29%2F2%5C7+=+5.44815499854966 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+51200+%29%29%2F2%5C7+=+5.44815499854966\"   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-%28150%29-sqrt%28+51200+%29%29%2F2%5C7+=+-26.8767264271211 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28150%29-sqrt%28+51200+%29%29%2F2%5C7+=+-26.8767264271211\"   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=7x%5E2%2B150x%2B-1025 ALIGN=MIDDLE  ALT=\"7x%5E2%2B150x%2B-1025\"   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=7x%5E2%2B150x%2B-1025+=+%28x-5.44815499854966%29%2A%28x--26.8767264271211%29 ALIGN=MIDDLE  ALT=\"7x%5E2%2B150x%2B-1025+=+%28x-5.44815499854966%29%2A%28x--26.8767264271211%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5.44815499854966, -26.8767264271211.\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+7%2Ax%5E2%2B150%2Ax%2B-1025+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B150%2Ax%2B-1025+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "===========<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-75%2F7+%2B+80%2Asqrt%282%29%2F7 ALIGN=MIDDLE  ALT=\"x+=+-75%2F7+%2B+80%2Asqrt%282%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-75%2F7+-+80%2Asqrt%282%29%2F7 ALIGN=MIDDLE  ALT=\"x+=+-75%2F7+-+80%2Asqrt%282%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub for x in the linear eqn and find y. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );