document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86430>Question 86430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to solve this equation by completing the square, and I'm a bit stumped. Any help would be greatly appreciated! \r<BR>\n" );
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document.write( "2x^2+10x+11=0\r<BR>\n" );
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document.write( "Thank you! \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62523 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=62523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "the general form of the quadratic equation is:\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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2%2B10%2Ax%2B11 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B10%2Ax%2B11\"   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+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A2%2A11+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A2%2A11+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=10, and c=11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+100-4%2A2%2A11+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+100-4%2A2%2A11+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 10 to get 100\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B-+sqrt%28+100%2B-88+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+100%2B-88+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A11%2A2 ALIGN=MIDDLE  ALT=\"-4%2A11%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-88 ALIGN=MIDDLE  ALT=\"-88\"   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+=+%28-10+%2B-+sqrt%28+12+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+sqrt%28+12+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under 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+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify 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+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B-+2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+%2B+2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+%2B+2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10+-+2%2Asqrt%283%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-10+-+2%2Asqrt%283%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.63397459621556 ALIGN=MIDDLE  ALT=\"x=-1.63397459621556\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.36602540378444 ALIGN=MIDDLE  ALT=\"x=-3.36602540378444\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.63397459621556 ALIGN=MIDDLE  ALT=\"x=-1.63397459621556\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.36602540378444 ALIGN=MIDDLE  ALT=\"x=-3.36602540378444\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2%2B10%2Ax%2B11 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2%2B10%2Ax%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-13.3660254037844%2C+8.36602540378444%2C+-13.3660254037844%2C+8.36602540378444%2C2%2Ax%5E2%2B10%2Ax%2B11%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on our calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.63397459621556 ALIGN=MIDDLE  ALT=\"x=-1.63397459621556\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3.36602540378444 ALIGN=MIDDLE  ALT=\"x=-3.36602540378444\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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