document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73546>Question 73546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x^2-x=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52611 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52611\">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=2x%5E2-x=6 ALIGN=MIDDLE  ALT=\"2x%5E2-x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The standard form for a quadratic equation is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You need to put your problem into that format.  Note that the only difference is that your<BR>\n" );
document.write( "problem has a constant on the right side instead of a zero.  So let's get rid of the 6 <BR>\n" );
document.write( "on the right side by subtracting 6 from both sides of the equation.  When you do that subtraction<BR>\n" );
document.write( "the result is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+x+-+6+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+x+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "There are several ways to solve this equation.  One of the ways is to find out if the <BR>\n" );
document.write( "equation can be factored.  Start by recognizing that the factors would have to have the<BR>\n" );
document.write( "first terms look like:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(2x   )*(x     )<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You have to find the numbers in each set of parenthesis that will make the factors multiply<BR>\n" );
document.write( "to give you back the equation of the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now look at the factors of 6.  There are two sets of them ... 6*1 and 3*2.  Because <BR>\n" );
document.write( "the 6 in the equation has a minus sign, one of the factors has to be negative. Notice in<BR>\n" );
document.write( "the equation that the middle term is minus x.  Whatever we select for the numbers in<BR>\n" );
document.write( "the factors will have to work together to give a minus -6 as the last number in the equation <BR>\n" );
document.write( "and a -x as the middle term.  Some trial and error is involved until you get enough <BR>\n" );
document.write( "experience to find a rapid way to do this. To save you some time the factors are:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29%2A%28x+-+2%29 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29%2A%28x+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you multiply these two together you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+x+-+6 ALIGN=MIDDLE  ALT=\"2x%5E2+-+x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the factors can be<BR>\n" );
document.write( "substituted for the left side our equation to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+3%29%2A%28x+-+2%29=+0 ALIGN=MIDDLE  ALT=\"%282x+%2B+3%29%2A%28x+-+2%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that if either factor on the left side is zero, it makes the left side of the equation<BR>\n" );
document.write( "equal the right side. (zero = zero)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Set the two factors (one at a time) equal to zero and solve for the value of x that makes<BR>\n" );
document.write( "it happen.  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"2x+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Subtract 3 from both sides and then divide that result by 2.  You will find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is one solution to the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next set the other factor equal to zero and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2+=+0 ALIGN=MIDDLE  ALT=\"x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Add 2 to both sides<BR>\n" );
document.write( "and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the second solution.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the answers to this problem are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope that this gives you a feel for one way to do these problems ... by factoring<BR>\n" );
document.write( "if the equation can be factored.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );