document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173854>Question 173854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve this equation using a quadratic formula can you help?<BR>\n" );
document.write( "4x^2=2x-11 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128728 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1: Put your equation into standard form:  <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2=2x-11 ALIGN=MIDDLE  ALT=\"4x%5E2=2x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8594; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-2x%2B11=0 ALIGN=MIDDLE  ALT=\"4x%5E2-2x%2B11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have <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=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=11 ALIGN=MIDDLE  ALT=\"c=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, substitute for a, b, and c into the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   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+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%284%29%2811%29+%29%29%2F%282%284%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%284%29%2811%29+%29%29%2F%282%284%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Then do the arithmetic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28+4-176+%29%29%2F8%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28+4-176+%29%29%2F8%29+\"   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+=+%282+%2B-+sqrt%28-172+%29%29%2F8%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28-172+%29%29%2F8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Oops! We have a negative number under the radical, so we have to invoke the imaginary number <i>i</i> defined as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   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+=+%282+%2B-+sqrt%28%28-1%29%2A172+%29%29%2F8%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28%28-1%29%2A172+%29%29%2F8%29+\"   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+=+%282+%2B-+sqrt%28i%5E2%2A172%29%29%2F8%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28i%5E2%2A172%29%29%2F8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And you need to find the factorization of 172:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2%2A43=172 ALIGN=MIDDLE  ALT=\"2%2A2%2A43=172\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B-+sqrt%28i%5E2%2A4%2A43%29%29%2F8%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt%28i%5E2%2A4%2A43%29%29%2F8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=%282%2B2i%2Asqrt%2843%29%29%2F8=%281%2Bi%2Asqrt%2843%29%29%2F4 ALIGN=MIDDLE  ALT=\"x%5B1%5D=%282%2B2i%2Asqrt%2843%29%29%2F8=%281%2Bi%2Asqrt%2843%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=%282-2i%2Asqrt%2843%29%29%2F8=%281-i%2Asqrt%2843%29%29%2F4 ALIGN=MIDDLE  ALT=\"x%5B2%5D=%282-2i%2Asqrt%2843%29%29%2F8=%281-i%2Asqrt%2843%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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