document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192184>Question 192184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I just want to doublecheck my answers if someone can help me.\r<BR>\n" );
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document.write( "Solve the following for x (use quadratic equation or factor out):<BR>\n" );
document.write( "4x^3-8x^2=0<BR>\n" );
document.write( "My answer was that there are No solutions to this problem\r<BR>\n" );
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document.write( "The other problem was:<BR>\n" );
document.write( "5x^2-3x+6=0<BR>\n" );
document.write( "My answer was the following:<BR>\n" );
document.write( "using the quadratic equation I came out with<BR>\n" );
document.write( "3-+SQRT(-3)^2-4(5)(6)/2(5)<BR>\n" );
document.write( "= 3-+SQRT111/10\r<BR>\n" );
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document.write( "Since the SQRT of 111 is 10.525 it would not be a R number, thereby No solution either.\r<BR>\n" );
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document.write( "Please let me know if I have that right; it would be greatly appreciated.<BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Gryhd </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144225 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^3-8x^2=0<BR>\n" );
document.write( "4x^2(x-2)=0<BR>\n" );
document.write( "x=0, x=2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5x^2-3x+6=0<BR>\n" );
document.write( "There is no real number answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed<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=5x%5E2%2B-3x%2B6+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-3x%2B6+=+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=%28-3%29%5E2-4%2A5%2A6=-111 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A5%2A6=-111\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -111 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 -111 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+111%29+=+10.5356537528527 ALIGN=MIDDLE  ALT=\"sqrt%28+111%29+=+10.5356537528527\"   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+-111+%29%29%2F2%5C5+=++%28--3%2B-i%2A10.5356537528527%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-3%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-3%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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