document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115423>Question 115423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each of the following quadratic equations by completing the square.<BR>\n" );
document.write( "2x2 + 10x + 11 = 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83996 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=83996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B10x%2B11=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x%2B11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B10x=-11 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 11 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2%2B5x%29=-11 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B5x%29=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient 2.  This step is important since we want the <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;\" > coefficient to be equal to 1.\r<BR>\n" );
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document.write( "Take half of the x coefficient 5 to get <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;\" >\r<BR>\n" );
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document.write( "Now square <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;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F4 ALIGN=MIDDLE  ALT=\"25%2F4\"   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=2%28x%5E2%2B5x%2B25%2F4%29=-11%2B%2825%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2%2B5x%2B25%2F4%29=-11%2B%2825%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F4 ALIGN=MIDDLE  ALT=\"25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x ALIGN=MIDDLE  ALT=\"x%5E2%2B5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  inside the parenthesis. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x%2B25%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x%2B25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a perfect square trinomial. Now add the result <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2825%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"%2825%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (remember we factored out a 2) to the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%2F2%29%5E2=-11%2B%2825%2F4%29%282%29 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F2%29%5E2=-11%2B%2825%2F4%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x%2B25%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x%2B25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F2%29%5E2\"   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=2%28x%2B5%2F2%29%5E2=-11%2B25%2F2 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F2%29%5E2=-11%2B25%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F4 ALIGN=MIDDLE  ALT=\"25%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 2 to get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F2 ALIGN=MIDDLE  ALT=\"25%2F2\"   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=2%28x%2B5%2F2%29%5E2=3%2F2 ALIGN=MIDDLE  ALT=\"2%28x%2B5%2F2%29%5E2=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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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;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F2=0%2B-sqrt%283%2F4%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F2=0%2B-sqrt%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F2=0%2B-sqrt%283%29%2Fsqrt%284%29 ALIGN=MIDDLE  ALT=\"x%2B5%2F2=0%2B-sqrt%283%29%2Fsqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5%2F2=0%2B-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"x%2B5%2F2=0%2B-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 4 to get 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F2%2B-sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"x=-5%2F2%2B-sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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 to isolate x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-5%2B-sqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-5%2B-sqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "So our answer is \r<BR>\n" );
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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;\" >  or <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;\" > \r<BR>\n" );
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