document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193042>Question 193042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have to find the solution... 2x^2+6x+5=0<BR>\n" );
document.write( "i have tried it with the completed square which means 2x^2+6x+9 = -5+9<BR>\n" );
document.write( "at the end i was with (2x+3)(x+3)=4 no complete square...<BR>\n" );
document.write( "then i tried to divide it by 2 so i had x^2 +3x+4.5=2<BR>\n" );
document.write( "but with 4.5 i am not getting a complete square either... \r<BR>\n" );
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document.write( "Now i don't know any further... PLEASE help me!\r<BR>\n" );
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document.write( "Anna </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144887 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=144887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i have to find the solution... 2x^2+6x+5=0<BR>\n" );
document.write( "i have tried it with the completed square which means 2x^2+6x+9 = -5+9<BR>\n" );
document.write( "at the end i was with (2x+3)(x+3)=4 no complete square...<BR>\n" );
document.write( "then i tried to divide it by 2 so i had x^2 +3x+4.5=2<BR>\n" );
document.write( "but with 4.5 i am not getting a complete square either... <BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Dividing by 2 is the best approach.<BR>\n" );
document.write( "x^2 +3x+2.5=0  Start from here<BR>\n" );
document.write( "x^2 + 3x + 2.25 = -0.25<BR>\n" );
document.write( "(x + 1.5)^2 = -0.25<BR>\n" );
document.write( "x+1.5 = +0.5i<BR>\n" );
document.write( "x+1.5 = -0.5i<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "x = -3/2 + i/2<BR>\n" );
document.write( "x = -3/2 - i/2<BR>\n" );
document.write( "------------<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%2B3x%2B2.5+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B3x%2B2.5+=+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=%283%29%5E2-4%2A1%2A2.5=-1 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A2.5=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -1 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 -1 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+1%29+=+1 ALIGN=MIDDLE  ALT=\"sqrt%28+1%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28-3%2B-i%2Asqrt%28+-1+%29%29%2F2%5C1+=++%28-3%2B-i%2A1%29%2F2%5C1+ ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28-3%2B-i%2Asqrt%28+-1+%29%29%2F2%5C1+=++%28-3%2B-i%2A1%29%2F2%5C1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<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+1%2Ax%5E2%2B3%2Ax%2B2.5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B2.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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