document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=774694>Question 774694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble telling if the equation has one, two, or no solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-15x%2B56=0 ALIGN=MIDDLE  ALT=\"x%5E2-15x%2B56=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #472379 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=472379\">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=x%5E2-15x%2B56=0 ALIGN=MIDDLE  ALT=\"x%5E2-15x%2B56=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....first factor completely so we can use zero product rule; write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15x ALIGN=MIDDLE  ALT=\"-15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-8x ALIGN=MIDDLE  ALT=\"-7x-8x\"   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%5E2-7x-8x%2B56+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-7x-8x%2B56+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-7x%29-%288x-56+%29=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2-7x%29-%288x-56+%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-7%29-8%28x-7+%29=+0 ALIGN=MIDDLE  ALT=\"x%28x-7%29-8%28x-7+%29=+0\"   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=%28x-8%29%28x-7%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-8%29%28x-7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have two real solutions\r<BR>\n" );
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document.write( "let's see them on a graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-2%2C+15%2C+-2%2C+10%2C+x%5E2-15x%2B56%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-2%2C+15%2C+-2%2C+10%2C+x%5E2-15x%2B56%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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