document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43873>Question 43873</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need steps and solution to this equation:\r<BR>\n" );
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document.write( "1/18h² - 1/2h + 1 = 0\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28786 by </B><A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><B>aaaaaaaa(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aaaaaaaa><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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=ah%5E2%2Bbh%2Bc=0 ALIGN=MIDDLE  ALT=\"ah%5E2%2Bbh%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0555555555555556h%5E2%2B-0.5h%2B1+=+0 ALIGN=MIDDLE  ALT=\"0.0555555555555556h%5E2%2B-0.5h%2B1+=+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=h%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"h%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" );
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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=%28-0.5%29%5E2-4%2A0.0555555555555556%2A1=0.0277777777777776 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-0.5%29%5E2-4%2A0.0555555555555556%2A1=0.0277777777777776\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=0.0277777777777776 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--0.5%2B-sqrt%28+0.0277777777777776+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--0.5%2B-sqrt%28+0.0277777777777776+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B1%5D+=+%28-%28-0.5%29%2Bsqrt%28+0.0277777777777776+%29%29%2F2%5C0.0555555555555556+=+5.99999999999999 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B2%5D+=+%28-%28-0.5%29-sqrt%28+0.0277777777777776+%29%29%2F2%5C0.0555555555555556+=+3 ALIGN=MIDDLE  ALT=\"h%5B2%5D+=+%28-%28-0.5%29-sqrt%28+0.0277777777777776+%29%29%2F2%5C0.0555555555555556+=+3\"   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=0.0555555555555556h%5E2%2B-0.5h%2B1 ALIGN=MIDDLE  ALT=\"0.0555555555555556h%5E2%2B-0.5h%2B1\"   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=0.0555555555555556h%5E2%2B-0.5h%2B1+=+0.0555555555555556%28h-5.99999999999999%29%2A%28h-3%29 ALIGN=MIDDLE  ALT=\"0.0555555555555556h%5E2%2B-0.5h%2B1+=+0.0555555555555556%28h-5.99999999999999%29%2A%28h-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5.99999999999999, 3.\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+0.0555555555555556%2Ax%5E2%2B-0.5%2Ax%2B1+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "The 5.999999999 is probably just a rounding error, caused by the neverending expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F18 ALIGN=MIDDLE  ALT=\"1%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You can consider it as 6. </SPAN>\n" );
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