document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=667139>Question 667139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to solve an equation by factoring.  The equation is:\r<BR>\n" );
document.write( "\n" );
document.write( "x^2/2  +  x/20  =  10\r<BR>\n" );
document.write( "\n" );
document.write( "What I have done is cleared the denominators and ended up with:\r<BR>\n" );
document.write( "\n" );
document.write( "10x^2  +  x  =  10\r<BR>\n" );
document.write( "\n" );
document.write( "Then I moved the 10 to the left side of the equation and ended up with:\r<BR>\n" );
document.write( "\n" );
document.write( "10x^2  +  x  -10  =  0\r<BR>\n" );
document.write( "\n" );
document.write( "I am stuck and cannot factor:  10x^2  +  x  -10\r<BR>\n" );
document.write( "\n" );
document.write( "The answer in the back of the book is:  {2/5, -1/2}, but am not sure how to get to this answer without successfully factoring first.\r<BR>\n" );
document.write( "\n" );
document.write( "In an attempt to factor, I multiplied the first and last coefficients and came up with -100.  There are no numbers that when multiplied together equal -100 and also equal the middle coefficient of 1 when added together.\r<BR>\n" );
document.write( "\n" );
document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #414816 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=414816\">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=+%28x%5E2%29%2F2+%2B+x%2F20+=+10+ ALIGN=MIDDLE  ALT=\"+%28x%5E2%29%2F2+%2B+x%2F20+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You are not simply changing the appearance<BR>\n" );
document.write( "of the fractions on the left side. This would be<BR>\n" );
document.write( "the case if you did:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%2F10%29%2A%28%28x%5E2%29%2F2%29+%2B+x%2F20+=+10+ ALIGN=MIDDLE  ALT=\"+%2810%2F10%29%2A%28%28x%5E2%29%2F2%29+%2B+x%2F20+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that you haven't really changed the value<BR>\n" );
document.write( "of the left side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+10x%5E2+%29%2F+20+%2B+x%2F20+=+200%2F20+ ALIGN=MIDDLE  ALT=\"+%28+10x%5E2+%29%2F+20+%2B+x%2F20+=+200%2F20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can multiply through by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x%5E2+%2B+x+=+200+ ALIGN=MIDDLE  ALT=\"+10x%5E2+%2B+x+=+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "What you wanted to do was multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%29%2F2+%2B+x%2F20+=+10+ ALIGN=MIDDLE  ALT=\"+%28x%5E2%29%2F2+%2B+x%2F20+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x%5E2+%2B+x+=+200+ ALIGN=MIDDLE  ALT=\"+10x%5E2+%2B+x+=+200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "same answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10x%5E2+%2B+x+-+200+=+0+ ALIGN=MIDDLE  ALT=\"+10x%5E2+%2B+x+-+200+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+10+ ALIGN=MIDDLE  ALT=\"+a+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1+ ALIGN=MIDDLE  ALT=\"+b+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-200+ ALIGN=MIDDLE  ALT=\"+c+=+-200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A10%2A%28-200%29+%29%29+%2F+%282%2A10%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A10%2A%28-200%29+%29%29+%2F+%282%2A10%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+=+%28-1+%2B-+sqrt%28+1+%2B+8000+%29%29+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+1+%2B+8000+%29%29+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B-+sqrt%28+8001+%29%29+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B-+sqrt%28+8001+%29%29+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-1+%2B+89.4483+%29+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-1+%2B+89.4483+%29+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+88.4483+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+88.4483+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4.4224+ ALIGN=MIDDLE  ALT=\"+x+=+4.4224+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-1+-+89.4483+%29+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-1+-+89.4483+%29+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-90.4483+%29+%2F+20+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-90.4483+%29+%2F+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-4.5224+ ALIGN=MIDDLE  ALT=\"+x+=+-4.5224+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+4.4224+%29%2A%28+x+%2B+4.5224+%29+ ALIGN=MIDDLE  ALT=\"+%28+x+-+4.4224+%29%2A%28+x+%2B+4.5224+%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+%2B+.1x+-+20+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+.1x+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+ ALIGN=MIDDLE  ALT=\"+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%29%2F2+%2B+x%2F20+-+10+=+0+ ALIGN=MIDDLE  ALT=\"+%28x%5E2%29%2F2+%2B+x%2F20+-+10+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%29%2F2+%2B+x%2F20+=+10+ ALIGN=MIDDLE  ALT=\"+%28x%5E2%29%2F2+%2B+x%2F20+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Why does the book disagree? I don't know<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );