document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976853>Question 976853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have an unsimplified equation and need to simplify it then solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+3sqrt%282%29+-+x+%29%2F%28+sqrt%28x%29+%29+=+sqrt%282x%29%2F+%28+sqrt%282%29+-+x+%29+ ALIGN=MIDDLE  ALT=\"%28+3sqrt%282%29+-+x+%29%2F%28+sqrt%28x%29+%29+=+sqrt%282x%29%2F+%28+sqrt%282%29+-+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so if I simplify using cross multiply I should have?:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+-+sqrt%282%29x+-+3sqrt%282%29x+%2B+x%5E2+=+sqrt%282%29x ALIGN=MIDDLE  ALT=\"6+-+sqrt%282%29x+-+3sqrt%282%29x+%2B+x%5E2+=+sqrt%282%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5sqrt%282%29x+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5sqrt%282%29x+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm new to doing this with square roots all involved, did I go about this right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598357 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=598357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have an unsimplified equation and need to simplify it then solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+3sqrt%282%29+-+x+%29%2F%28+sqrt%28x%29+%29+=+sqrt%282x%29%2F+%28+sqrt%282%29+-+x+%29+ ALIGN=MIDDLE  ALT=\"%28+3sqrt%282%29+-+x+%29%2F%28+sqrt%28x%29+%29+=+sqrt%282x%29%2F+%28+sqrt%282%29+-+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so if I simplify using cross multiply I should have?:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+-+sqrt%282%29x+-+3sqrt%282%29x+%2B+x%5E2+=+sqrt%282%29x ALIGN=MIDDLE  ALT=\"6+-+sqrt%282%29x+-+3sqrt%282%29x+%2B+x%5E2+=+sqrt%282%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5sqrt%282%29x+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5sqrt%282%29x+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I'm new to doing this with square roots all involved, did I go about this right?<BR>\n" );
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document.write( "Looks right.  Solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+5sqrt%282%29x+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+5sqrt%282%29x+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6+=+5sqrt%282%29x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6+=+5sqrt%282%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+12x%5E2+%2B+36+=+50x%5E2 ALIGN=MIDDLE  ALT=\"x%5E4+%2B+12x%5E2+%2B+36+=+50x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+38x%5E2+%2B+36+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-+38x%5E2+%2B+36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "Sub u for x^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+-+38u+%2B+36+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+-+38u+%2B+36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=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-38x%2B36+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-38x%2B36+=+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=%28-38%29%5E2-4%2A1%2A36=1300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-38%29%5E2-4%2A1%2A36=1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1300 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--38%2B-sqrt%28+1300+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--38%2B-sqrt%28+1300+%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-%28-38%29%2Bsqrt%28+1300+%29%29%2F2%5C1+=+37.0277563773199 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-38%29%2Bsqrt%28+1300+%29%29%2F2%5C1+=+37.0277563773199\"   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-%28-38%29-sqrt%28+1300+%29%29%2F2%5C1+=+0.972243622680054 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-38%29-sqrt%28+1300+%29%29%2F2%5C1+=+0.972243622680054\"   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-38x%2B36 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-38x%2B36\"   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-38x%2B36+=+%28x-37.0277563773199%29%2A%28x-0.972243622680054%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-38x%2B36+=+%28x-37.0277563773199%29%2A%28x-0.972243622680054%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 37.0277563773199, 0.972243622680054.\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-38%2Ax%2B36+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-38%2Ax%2B36+%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( "x^2 = answers shown<BR>\n" );
document.write( "Find the sq roots.<BR>\n" );
document.write( "Check for extraneous solutions.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );