document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184612>Question 1184612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the quadratic equation below using the appropriate method. Show your work or solution.\r<BR>\n" );
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document.write( "x ^ 2 - 2x - 8 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815256 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The reference provided by the other tutor is, in my opinion, not a particularly good one.  It shows SOLVING several example quadratic equations; but it doesn't provide much explanation on HOW TO SOLVE them.<br><BR>\n" );
document.write( "The instructions for this problem say to solve using \"the appropriate method\".<br><BR>\n" );
document.write( "It is unclear what \"the appropriate\" method is; different students will use different methods.<br><BR>\n" );
document.write( "You can ALWAYS solve a quadratic equation using the quadratic formula.  However, the probable intent of this problem is to provide practice in solving by factoring.<br><BR>\n" );
document.write( "So let's take a look at what is involved in solving by factoring.<br><BR>\n" );
document.write( "We want to factor x^2-2x-8 into the form (x+a)(x+b) where a and b are integers.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%28x%2Bb%29=x%5E2%2Bax%2Bbx%2Bab+=+x%5E2%2B%28a%2Bb%29x%2B%28ab%29+=+x%5E2-2x-8 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%28x%2Bb%29=x%5E2%2Bax%2Bbx%2Bab+=+x%5E2%2B%28a%2Bb%29x%2B%28ab%29+=+x%5E2-2x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We see that our two numbers a and b have to be such that<BR>\n" );
document.write( "(1) their sum a+b is -2; and<BR>\n" );
document.write( "(2) their product ab is -8<br><BR>\n" );
document.write( "Clearly the product ab=-8 means one of the numbers is positive and one negative.  Then playing around with possible values of a and b to give a product of -8 and a sum of -2 gives us -4 and 2 as the two numbers.  So the factorization is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-8=%28x-4%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8=%28x-4%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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