document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163331>Question 163331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this problem?  I am stumped!\r<BR>\n" );
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document.write( "Find a value for k that will make 4x^2+6.4x+k a perfect square.  I need to describe the procedure that I used.\r<BR>\n" );
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document.write( "All I can figure so far is:<BR>\n" );
document.write( "k=?<BR>\n" );
document.write( "4x^2+6.4x+k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120343 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^2+6.4x+k=0  divide each term by 4<BR>\n" );
document.write( "x^2+(6.4/4)x+k/4=0----eq1\r<BR>\n" );
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document.write( "Let (x+a)^2 be the solution to this quadratic<BR>\n" );
document.write( "expand, using foil:<BR>\n" );
document.write( "x^2+xa+xa+a^2=<BR>\n" );
document.write( "x^2+2xa+a^2=0-------eq2<BR>\n" );
document.write( "Now we know that eq2 has to be identical to eq1 in all respects, so:<BR>\n" );
document.write( "2a=(6.4/4) divide each side by 2<BR>\n" );
document.write( "a=(6.4/8)-------eq3<BR>\n" );
document.write( "a^2=k/4-----------eq4\r<BR>\n" );
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document.write( "substitute eq3 into eq4<BR>\n" );
document.write( "(6.4/8)^2=k/4 or<BR>\n" );
document.write( "40.96/64=k/4   multiply each side by 4<BR>\n" );
document.write( "k=40.96/16<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "x^2+(6.4/4)x+(40.96/64)<BR>\n" );
document.write( "(x+6.4/8)^2  expand using foil<BR>\n" );
document.write( "x^2+(6.4/8)x+(6.4/8)x+(6.4/8)^2=<BR>\n" );
document.write( "x^2+(6.4/4)x+40.96/64\r<BR>\n" );
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document.write( "We can work this problem without dividing each term by 4 as we did initially.<BR>\n" );
document.write( "4x^2+6.4x+k----------------eq1a<BR>\n" );
document.write( "Let (ax+b)^2 be the solution ( a perfect square) expand using foil<BR>\n" );
document.write( "a^2x^2+abx+abx+b^2 or<BR>\n" );
document.write( "a^2x^2+2abx+b^2-----again, this must be identical to eq1a, so:\r<BR>\n" );
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document.write( "a^2=4-------------eq2a\r<BR>\n" );
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document.write( "2ab=6.4-----------eq3a divide each side by 2a<BR>\n" );
document.write( "b=6.4/2a-------substitute this into eq4a\r<BR>\n" );
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document.write( "and b^2=k-----eq4a<BR>\n" );
document.write( "(6.4/2a)^2=k<BR>\n" );
document.write( "(40.96/4a^2)=k  but from eq2a, a^2=4, therefore<BR>\n" );
document.write( "k=(40.96/16)-------------------------same as before\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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