document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=227951>Question 227951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-4x%2B3=0+ ALIGN=MIDDLE  ALT=\"+4x%5E2-4x%2B3=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169314 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=169314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-4x%2B3=0 ALIGN=MIDDLE  ALT=\"4x%5E2-4x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-4x%2B3 ALIGN=MIDDLE  ALT=\"4x%5E2-4x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-4 ALIGN=MIDDLE  ALT=\"B=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3 ALIGN=MIDDLE  ALT=\"C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-4 ALIGN=MIDDLE  ALT=\"B=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3 ALIGN=MIDDLE  ALT=\"C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%283%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+16-4%284%29%283%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16-4%284%29%283%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+16-48+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+16-48+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%283%29 ALIGN=MIDDLE  ALT=\"4%284%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+sqrt%28+-32+%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284+%2B-+4i%2Asqrt%282%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%284+%2B-+4i%2Asqrt%282%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284%2B4i%2Asqrt%282%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%284%2B4i%2Asqrt%282%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284-4i%2Asqrt%282%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%284-4i%2Asqrt%282%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281-i%2Asqrt%282%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%281-i%2Asqrt%282%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2Bi%2Asqrt%282%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281-i%2Asqrt%282%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%281-i%2Asqrt%282%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: if you have no idea what the 'i' terms are all about, then you probably haven't learned about imaginary numbers yet. If that's the case, then there are no solutions to this problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );