document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66056>Question 66056</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131482874/algebrahomeworkh>beginning algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I'm supposed to solve for the roots of each quadratic equation by using the factoring method.  This is so confusing to me it's almost painful.  I honestly d^2+3x-40=0 on't know where to start.<BR>\n" );
document.write( "Xis the problem.  If you could get this to make sense to me I would greatly appreciate it.\r<BR>\n" );
document.write( "\n" );
document.write( "Karen </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46793 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=46793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have either one of two problems<BR>\n" );
document.write( "Either you have:<BR>\n" );
document.write( "(1) The blank stare mental paralysis drifting off to daydream problem<BR>\n" );
document.write( "or, almost as bad<BR>\n" );
document.write( "(2) The jump in with both feet without a plan problem<BR>\n" );
document.write( "(2) usually leads to (1)<BR>\n" );
document.write( "Start off with what you know for sure. You know the answer will<BR>\n" );
document.write( "generally look like this:<BR>\n" );
document.write( "(_____plus or minus_____)(_____plus or minus_____) = 0<BR>\n" );
document.write( "I recommend you do just what I did. Write down the <BR>\n" );
document.write( "parentheses with nothing in them yet and the \"= 0\"<BR>\n" );
document.write( "Now figure out what the signs should be. Look at<BR>\n" );
document.write( "the problem. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+3x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+-+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. There's only two ways you can get <BR>\n" );
document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40 ALIGN=MIDDLE  ALT=\"-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, + times -, or, - times +, so put in one of those.<BR>\n" );
document.write( "(____ + ____)(____ - ____) = 0. This is what you know for sure so far.<BR>\n" );
document.write( "and you can do it with any factoring problem. Lots better than a blank<BR>\n" );
document.write( "stare.<BR>\n" );
document.write( "Now look at the <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;\" >. The factors are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If it was<BR>\n" );
document.write( "say, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2 ALIGN=MIDDLE  ALT=\"10x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the factors might be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x ALIGN=MIDDLE  ALT=\"5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x ALIGN=MIDDLE  ALT=\"10x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but your problem is easier.<BR>\n" );
document.write( "OK, so far you have<BR>\n" );
document.write( "( x + ____)( x - ____) = 0<BR>\n" );
document.write( "Now you have to do a little head-scratching, but it's really not that bad.<BR>\n" );
document.write( "All you need to remember about factoring is that each term in the first<BR>\n" );
document.write( "gets multiplied by each term in the second, so if I had<BR>\n" );
document.write( "(a + b)(c + d - e + f) I'd get ac + ad - ae + af + bc + bd - be + bf<BR>\n" );
document.write( "Look at the middle term, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, The sign is positive. That means <BR>\n" );
document.write( "that whatever factors you decide on for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40 ALIGN=MIDDLE  ALT=\"-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the + factor should<BR>\n" );
document.write( "be the greatest. Look at all the possibilities<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40%2A%28%2B1%29+=+-40 ALIGN=MIDDLE  ALT=\"-40%2A%28%2B1%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B40%2A%28-1%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B40%2A%28-1%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20%2A%28%2B2%29+=+-40 ALIGN=MIDDLE  ALT=\"-20%2A%28%2B2%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B20%2A%28-2%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B20%2A%28-2%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%2A%28%2B4%29+=+-40 ALIGN=MIDDLE  ALT=\"-10%2A%28%2B4%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10%2A%28-4%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B10%2A%28-4%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2A%28%2B5%29+=+-40 ALIGN=MIDDLE  ALT=\"-8%2A%28%2B5%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B8%2A%28-5%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B8%2A%28-5%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But I said the greatest factor should be +, so that leaves us<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B40%2A%28-1%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B40%2A%28-1%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B20%2A%28-2%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B20%2A%28-2%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10%2A%28-4%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B10%2A%28-4%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B8%2A%28-5%29+=+-40 ALIGN=MIDDLE  ALT=\"%2B8%2A%28-5%29+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Try these one by one and see what the middle term ends up being<BR>\n" );
document.write( "( x + 40)( x - 1) = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B40x+-+x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B40x+-+x+-+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+%2B+39x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+39x+-+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so, that's not it<BR>\n" );
document.write( "(x + 20)(x - 2) = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+20x+-+2x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+20x+-+2x+-+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+%2B+18x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+18x+-+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Closer, but that's not it either<BR>\n" );
document.write( "(x + 10)(x - 4) = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+10x+-4x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+10x+-4x+-+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+%2B+6x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+-+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Closest so far, still not right<BR>\n" );
document.write( "(x + 8)(x - 5) = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+8x+-+5x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+8x+-+5x+-+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+%2B+3x+-+40+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+3x+-+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Bingo! Just go step by step. Notice that 8 - 5 = 3 is the key, but<BR>\n" );
document.write( "going step by step will always get you there with no blank stares. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );