document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752011>Question 752011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A number is 1 more than twice another.  Their squares differ by 176.  What are the numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #457521 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=457521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll call them x and y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   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-y%5E2=176 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=176\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%282x%2B1%29%5E2=176 ALIGN=MIDDLE  ALT=\"x%5E2-%282x%2B1%29%5E2=176\"   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-%284x%5E2%2B4x%2B1%29=176 ALIGN=MIDDLE  ALT=\"x%5E2-%284x%5E2%2B4x%2B1%29=176\"   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=-3x%5E2-4x-177=0 ALIGN=MIDDLE  ALT=\"-3x%5E2-4x-177=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\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=3x%5E2%2B4x%2B177+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B4x%2B177+=+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=%284%29%5E2-4%2A3%2A177=-2108 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A3%2A177=-2108\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  The discriminant -2108 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -2108 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+2108%29+=+45.912961132996 ALIGN=MIDDLE  ALT=\"sqrt%28+2108%29+=+45.912961132996\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
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document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28-4%2B-+i%2Asqrt%28+-2108+%29%29%2F2%5C3+=++%28-4%2B-+i%2A45.912961132996%29%2F2%5C3+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\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+3%2Ax%5E2%2B4%2Ax%2B177+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B4%2Ax%2B177+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "so we see that no pair of real numbers wtii work but\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%281%2F3%29%2A%28-2+%2B-+i+%2Asqrt%28527%29%29%0D%0A ALIGN=MIDDLE  ALT=\"%0D%0A%281%2F3%29%2A%28-2+%2B-+i+%2Asqrt%28527%29%29%0D%0A\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "does work\r<BR>\n" );
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document.write( ":) </SPAN>\n" );
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