document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65770>Question 65770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the quadratic equation by completing the square:<BR>\n" );
document.write( "2x^2 + 10x + 11 = 0\r<BR>\n" );
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document.write( "Can someone please explain to me the idea behind the quadratic equation, 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 #46495 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=46495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation is one in which the highest power of the independent variable (x in this case) is 2.  Quadratic comes from the latin \"Quadra\" meanining square.\r<BR>\n" );
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document.write( "Solve by completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2A2+%2B10x+%2B+11+=+0 ALIGN=MIDDLE  ALT=\"2x%2A2+%2B10x+%2B+11+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > First,divide through by 2 in order to get the coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5x+%2B+11%2F2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5x+%2B+11%2F2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Next, subtract 11/2 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5x+=+-11%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5x+=+-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add to both sides, the square of half the coefficient of x. This is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F2%29%5E2+=+25%2F4 ALIGN=MIDDLE  ALT=\"%285%2F2%29%5E2+=+25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+5x+%2B+25%2F4+=+%2825%2F4%29-11%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+5x+%2B+25%2F4+=+%2825%2F4%29-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now simplify this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F2%29%5E2+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F2%29%5E2+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F2+=+sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F2+=+sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have a + or - in front of it. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2F2%29%2B-sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2F2%29%2B-sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5%2Bsqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-5%2Bsqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.63397 (Approx.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-5-sqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-5-sqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -3.36603 (Approx.)\r<BR>\n" );
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