document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172888>Question 1172888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by factoring.\r<BR>\n" );
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document.write( "25x squared + 30x + 8 = 0\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798062 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=798062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Two other tutors have shown methods for factoring quadratics like this one using different purely algebraic methods.<br><BR>\n" );
document.write( "Both methods are good; and there are many other similar methods.  But I prefer the basic method that -- at least when I was learning algebra 60 years ago -- was always used.<br><BR>\n" );
document.write( "We want to factor the expression as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B30x%2B8+=+%28ax%2Bb%29%28cx%2Bd%29 ALIGN=MIDDLE  ALT=\"25x%5E2%2B30x%2B8+=+%28ax%2Bb%29%28cx%2Bd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where a, b, c, and d are integers.<br><BR>\n" );
document.write( "The positive constant term 8 tells us the constants b and d are the same sign; then the positive linear term 30x tells us b and d are both positive.<br><BR>\n" );
document.write( "a and c have to multiply to 25; and b and d have to multiply to 8.  There are not many possibilities:<BR>\n" );
document.write( "a and c are 25 and 1, or 5 and 5<BR>\n" );
document.write( "b and d are 1 and 8, or 2 and 4, or 4 and 2, or 8 and 1<br><BR>\n" );
document.write( "Try different combinations until you find the one that gives the correct middle term, 30x.<br><BR>\n" );
document.write( "Fast and easy calculations show the answer to be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B30x%2B8+=+%285x%2B4%29%285x%2B2%29 ALIGN=MIDDLE  ALT=\"25x%5E2%2B30x%2B8+=+%285x%2B4%29%285x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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