document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136355>Question 136355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me please. It asks to solve by completing the square.<BR>\n" );
document.write( "x^2-x-1=0<BR>\n" );
document.write( "What I got for that was (y=a) (a=1) (H=1/2) and (k=5/4)<BR>\n" );
document.write( "I am not sure if they are correct or not, please help,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 #99874 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Help me please. It asks to solve by completing the square.<BR>\n" );
document.write( "x^2-x-1=0<BR>\n" );
document.write( "What I got for that was (y=a) (a=1) (H=1/2) and (k=5/4)<BR>\n" );
document.write( "I am not sure if they are correct or not, please help,Thank You=)\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Get rid of the constant term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1 ALIGN=MIDDLE  ALT=\"%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to both sides:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=1 ALIGN=MIDDLE  ALT=\"x%5E2-x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the coefficient of x on the left, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, getting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F2%29%5E2=1%2F4 ALIGN=MIDDLE  ALT=\"%28-1%2F2%29%5E2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2B1%2F4=1%2B+1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=1%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "write the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2B1%2F4=1%2F1%2B+1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=1%2F1%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The LCD on the right is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4 ALIGN=MIDDLE  ALT=\"4%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=x%5E2-x%2B1%2F4=+++%281%2F1+%29%2A%284%2F4%29%2B+1%2F4++ ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=+++%281%2F1+%29%2A%284%2F4%29%2B+1%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=x%5E2-x%2B1%2F4=4%2F4%2B+1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=4%2F4%2B+1%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=x%5E2-x%2B1%2F4=5%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-x%2B1%2F4=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now factor the left side:\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F2%29%28x-1%2F2%29=5%2F4 ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%28x-1%2F2%29=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The left side is a perfect square (that's why the method is<BR>\n" );
document.write( "called \"completing the square\").  So we write the left side<BR>\n" );
document.write( "as a square, the square of a binomial:\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F2%29%5E2=5%2F4 ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next we use the principle of square roots:\r<BR>\n" );
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document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2 ALIGN=MIDDLE  ALT=\"x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2 ALIGN=MIDDLE  ALT=\"x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2 ALIGN=MIDDLE  ALT=\"x-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we solve for x by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:\r<BR>\n" );
document.write( "\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%2F2%2B1%2F2 ALIGN=MIDDLE  ALT=\"x-1%2F2%2B1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B-sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"1%2F2%2B-sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "            <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2%2B-sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"1%2F2%2B-sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );