document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475389>Question 475389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem: Solve using the quadratic formula: 5x(squared)-2x+9=0\r<BR>\n" );
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document.write( "x= 2 times the square root of 2(squared)-4(5)(9) over 5(2).<BR>\n" );
document.write( "x= 2 times the square root of 4-180 over 10.<BR>\n" );
document.write( "x= 2 times +or- the square root of -176 over 10.<BR>\n" );
document.write( "x= +or- the square root of -176 over 5.\r<BR>\n" );
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document.write( "That is as far as I've gotten in the problem.  I know that the answer is supposed to be 1/5 +- 2(square root of 11)/5i.  I'm having a difficult time figuring out how to get there from the last step of the problem I listed.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325993 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=325993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve using the quadratic formula: <BR>\n" );
document.write( "5x^2-2x+9=0\r<BR>\n" );
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document.write( "x= 2 times the square root of 2(squared)-4(5)(9) over 5(2)<BR>\n" );
document.write( "-------- It's 2 ± the sqrt .... , not times.<BR>\n" );
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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=5x%5E2%2B-2x%2B9+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-2x%2B9+=+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=%28-2%29%5E2-4%2A5%2A9=-176 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A5%2A9=-176\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -176 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 -176 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+176%29+=+13.2664991614216 ALIGN=MIDDLE  ALT=\"sqrt%28+176%29+=+13.2664991614216\"   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--2%2B-i%2Asqrt%28+-176+%29%29%2F2%5C5+=++%28--2%2B-i%2A13.2664991614216%29%2F2%5C5+ ALIGN=MIDDLE   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+5%2Ax%5E2%2B-2%2Ax%2B9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-2%2Ax%2B9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "x= 2 times the square root of 4-180 over 10.<BR>\n" );
document.write( "x= 2 times +or- the square root of -176 over 10.<BR>\n" );
document.write( "x= +or- the square root of -176 over 5.\r<BR>\n" );
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document.write( "That is as far as I've gotten in the problem.  I know that the answer is supposed to be 1/5 +- 2(square root of 11)/5i.  I'm having a difficult time figuring out how to get there from the last step of the problem I listed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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