document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629638>Question 629638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the equation x^2-15-k(2x-8)=0has equal roots find the value of k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #396389 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=396389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the roots are equal, the equation  looks<BR>\n" );
document.write( "like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+a+%29%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+%28+x+-+a+%29%5E2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then there are 2 roots <BR>\n" );
document.write( "at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+a+ ALIGN=MIDDLE  ALT=\"+x+=+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+a+%29%5E2+=+x%5E2+-+15+-+k%2A%28+2x+-+8+%29+ ALIGN=MIDDLE  ALT=\"+%28+x+-+a+%29%5E2+=+x%5E2+-+15+-+k%2A%28+2x+-+8+%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%5E2+-+2a%2Ax+%2B+a%5E2+=+x%5E2+-+2k%2Ax+-+15+%2B+8k+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+2a%2Ax+%2B+a%5E2+=+x%5E2+-+2k%2Ax+-+15+%2B+8k+\"   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+-+2a%2Ax+%2B+a%5E2+=+x%5E2+-+2k%2Ax+%2B+%28+8k+-+15+%29+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+2a%2Ax+%2B+a%5E2+=+x%5E2+-+2k%2Ax+%2B+%28+8k+-+15+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Matching up coefficients:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+a+ ALIGN=MIDDLE  ALT=\"+k+=+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%5E2+=+8k+-+15+ ALIGN=MIDDLE  ALT=\"+a%5E2+=+8k+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By substitution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2+=+8k+-+15+ ALIGN=MIDDLE  ALT=\"+k%5E2+=+8k+-+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k%5E2+-+8k+%2B+15+=+0+ ALIGN=MIDDLE  ALT=\"+k%5E2+-+8k+%2B+15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+k+-+3+%29%2A%28+k+-+5+%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28+k+-+3+%29%2A%28+k+-+5+%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=+k+=+3+ ALIGN=MIDDLE  ALT=\"+k+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+5+ ALIGN=MIDDLE  ALT=\"+k+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------<BR>\n" );
document.write( "check answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+15+-+k%2A%28+2x+-+8+%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+k%2A%28+2x+-+8+%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+-+15+-+3%2A%28+2x+-+8+%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+3%2A%28+2x+-+8+%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+-+15+-+6x+%2B+24+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+6x+%2B+24+=+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+-+6x+%2B+9+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+6x+%2B+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+3+%29%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+%28+x+-+3+%29%5E2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+3+ ALIGN=MIDDLE  ALT=\"+k+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > works<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+15+-+k%2A%28+2x+-+8+%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+k%2A%28+2x+-+8+%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+-+15+-+5%2A%28+2x+-+8+%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+5%2A%28+2x+-+8+%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+-+15+-+10x+%2B+40+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+15+-+10x+%2B+40+=+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+-+10x+%2B+25+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+10x+%2B+25+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+5+%29%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+%28+x+-+5+%29%5E2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+5+ ALIGN=MIDDLE  ALT=\"+k+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > works too </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );