document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121710>Question 121710</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of c so that the quadratic equation 2x^2+4x-c=0 has two equal real roots. Can someone please help me ? I think the answer is -1/2 but I'm not sure ?!!? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89355 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=89355\">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%2B4x-c=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x-c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To have two equal real roots, the equation has to be of the form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-a%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "with 2 real roots at x=a. <BR>\n" );
document.write( "If we expand that equation, we can compare terms with the original equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%5E2=x%5E2-2a%2Ba%5E2 ALIGN=MIDDLE  ALT=\"%28x-a%29%5E2=x%5E2-2a%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's multiply by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-a%29%5E2=2x%5E2-4a%2B2a%5E2 ALIGN=MIDDLE  ALT=\"2%28x-a%29%5E2=2x%5E2-4a%2B2a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's compare. <BR>\n" );
document.write( "1.<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;\" > term : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=2x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2=2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > term : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2ax=4x ALIGN=MIDDLE  ALT=\"-2ax=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=constant ALIGN=MIDDLE  ALT=\"constant\"   DISABLED_style= \"max-width:90%; height:auto;\" > term : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2=-c ALIGN=MIDDLE  ALT=\"2a%5E2=-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2ax=4x ALIGN=MIDDLE  ALT=\"-2ax=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2a=4 ALIGN=MIDDLE  ALT=\"-2a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2=-c ALIGN=MIDDLE  ALT=\"2a%5E2=-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2a%5E2 ALIGN=MIDDLE  ALT=\"c=-2a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2%28-2%29%5E2 ALIGN=MIDDLE  ALT=\"c=-2%28-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2%284%29 ALIGN=MIDDLE  ALT=\"c=-2%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-8 ALIGN=MIDDLE  ALT=\"c=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );