document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156565>Question 156565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 9. Using Factoring, how do I complete this exercise?\r<BR>\n" );
document.write( "\n" );
document.write( "25x^2 + 20x + 4\r<BR>\n" );
document.write( "\n" );
document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115315 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=115315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> None of the coefficients have anything in common besides 1. So, we are going to need a 5 coefficient for a,c in (ax+b)(cx+d) factorization.<BR>\n" );
document.write( "So we need (5x+b)(5x+d)=25x^2+20x+4. We can suspect b=d=2 because if b=4, our x coefficient becomes >20. So (5x+2)^2 is our factorization.\r<BR>\n" );
document.write( "\n" );
document.write( "Now, we could solve this slightly differently, yet more concisely:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(5x+b)(5x+d)=25x^2+20x+4<BR>\n" );
document.write( "25x^2+5xd+5xb+bd=25x^2+20x+4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that:<BR>\n" );
document.write( "5d+5b=20<BR>\n" );
document.write( "bd=4\r<BR>\n" );
document.write( "\n" );
document.write( "from the first equation: d=4-b<BR>\n" );
document.write( "putting that into the second equation: b(4-b)=4<BR>\n" );
document.write( "4b-b^2-4=0<BR>\n" );
document.write( "b^2-4b+4=0\r<BR>\n" );
document.write( "\n" );
document.write( "We must necessarily have solution b=2 and d=4-2=2 as well. So we place those values in our hybrid form, getting the answer already supplied. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );