document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034331>Question 1034331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following quadratic equation by factoring (find zeroes)\r<BR>\n" );
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document.write( "2x^2-2x-4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648945 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ -\ 2x\ -\ 4\ =\ 0\">\r<BR>\n" );
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document.write( "First take out the common integer factor, 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\left(x^2\ -\ x\ -\ 2\right)\ =\ 0\">\r<BR>\n" );
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document.write( "We are now looking for two binomial factors that have the following characteristics:\r<BR>\n" );
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document.write( "1.  The product of the constant terms is negative 2.\r<BR>\n" );
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document.write( "2.  The sum of the constant terms is negative 1.\r<BR>\n" );
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document.write( "Since the product is negative, the two constant terms must be of opposite sign.  The only two integers that have a product of 2 are 2 and 1, so we know that we are looking for either 2 times -1 or -2 times 1.\r<BR>\n" );
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document.write( "Since 2 plus -1 is 1, we can discard this choice because we are looking for a sum of -1.  -2 plus 1 is -1, so the two integers must be -2 and 1.\r<BR>\n" );
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document.write( "That makes the two factors <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ 2)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 1)\">\r<BR>\n" );
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document.write( "Putting it all back together we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\left((x\ -\ 2)(x\ +\ 1)\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Now you have 3 factors whose product is zero.  That means one of the factors must be zero.  We can eliminate 2 because 2 is not and never will be zero.  That leaves <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ 2)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 1)\">, either of which could be zero given an appropriate value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ 2)\ =\ 0\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 2\">\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 1)\ =\ 0\"> then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -1\">\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2(2)^2\ -\ 2(2)\ -\ 4\ =^?\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8\ -\ 4\ -\ 4\ =\ 0\">  Checks.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2(-1)^2\ -\ 2(-1)\ -\ 4\ =^?\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ +\ 2\ -\ 4\ =\ 0\">  Checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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