document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135529>Question 135529</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value of c will the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B12x%2Bc=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B12x%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > have one distinct solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99297 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=99297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B12x%2Bc=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B12x%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have one distinct solution if the discriminant equals zero. In other words, when  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Notice how a=1, b=12, and c=c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29%5E2-4%281%29c=0 ALIGN=MIDDLE  ALT=\"%2812%29%5E2-4%281%29c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1 and b=12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144-4c=0 ALIGN=MIDDLE  ALT=\"144-4c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square and multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4c=0-144 ALIGN=MIDDLE  ALT=\"-4c=0-144\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 144 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4c=-144 ALIGN=MIDDLE  ALT=\"-4c=-144\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28-144%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"c=%28-144%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -4 to isolate c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=36 ALIGN=MIDDLE  ALT=\"c=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=36 ALIGN=MIDDLE  ALT=\"c=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B12x%2B36=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B12x%2B36=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have one distinct solution\r<BR>\n" );
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