document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108379>Question 108379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> completing the square\r<BR>\n" );
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document.write( "-1/2x²+4x-6=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #79012 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79012\">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=-%281%2F2%29x%5E2%2B4x-6=0 ALIGN=MIDDLE  ALT=\"-%281%2F2%29x%5E2%2B4x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's multiply both sides by (-2) to get rid of the fraction. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%29%28-%281%2F2%29x%5E2%2B4x-6%29=0 ALIGN=MIDDLE  ALT=\"%28-2%29%28-%281%2F2%29x%5E2%2B4x-6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify.<BR>\n" );
document.write( "We want to find a constant, a, such that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Expand the perfect square equation. <BR>\n" );
document.write( "Compare coefficients of that equation with your equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ax=-8x ALIGN=MIDDLE  ALT=\"2ax=-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "If a=-4, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=16 ALIGN=MIDDLE  ALT=\"a%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "In order get get 16 on the left hand side of the equation, that is, in order to complete the square, you need to add 4 to the left hand side. <BR>\n" );
document.write( "Whatever you do to one side of the equation, you must do to the other side. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B12=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2B16=4 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2B16=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 4 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >Complete the square. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=2 ALIGN=MIDDLE  ALT=\"x-4=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=-2 ALIGN=MIDDLE  ALT=\"x-4=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=2 ALIGN=MIDDLE  ALT=\"x-4=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=-2 ALIGN=MIDDLE  ALT=\"x-4=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Check your answers. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29x%5E2%2B4x-6=0 ALIGN=MIDDLE  ALT=\"-%281%2F2%29x%5E2%2B4x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29%286%29%5E2%2B4%286%29-6=0 ALIGN=MIDDLE  ALT=\"-%281%2F2%29%286%29%5E2%2B4%286%29-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%2B24-6=0 ALIGN=MIDDLE  ALT=\"-18%2B24-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29x%5E2%2B4x-6=0 ALIGN=MIDDLE  ALT=\"-%281%2F2%29x%5E2%2B4x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29%282%29%5E2%2B4%282%29-6=0 ALIGN=MIDDLE  ALT=\"-%281%2F2%29%282%29%5E2%2B4%282%29-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B8-6=0 ALIGN=MIDDLE  ALT=\"-2%2B8-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both answers lead to true statements.<BR>\n" );
document.write( "Good answers. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );