document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=236845>Question 236845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem:\r<BR>\n" );
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document.write( "Find k to make the trinomial a perfect square:\r<BR>\n" );
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document.write( "r square + 10r + k\r<BR>\n" );
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document.write( "Thank you, Carrie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174233 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=174233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, perfect squares are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case, we want a perfect square of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Bx%29%5E2 ALIGN=MIDDLE  ALT=\"%28r%2Bx%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where 'x' is an unknown expression or number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Bx%29%5E2=r%5E2%2B10r%2Bk ALIGN=MIDDLE  ALT=\"%28r%2Bx%29%5E2=r%5E2%2B10r%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set that perfect square expression equal to the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2B2rx%2Bx%5E2=r%5E2%2B10r%2Bk ALIGN=MIDDLE  ALT=\"r%5E2%2B2rx%2Bx%5E2=r%5E2%2B10r%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2rx%2Bx%5E2=10r%2Bk ALIGN=MIDDLE  ALT=\"2rx%2Bx%5E2=10r%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "Since the only terms with 'r' in them are 2rx and 10r, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2rx=10r ALIGN=MIDDLE  ALT=\"2rx=10r\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Divide both sides by 'r' to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=10 ALIGN=MIDDLE  ALT=\"2x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now solve for 'x' to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the left side of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2Bx%29%5E2 ALIGN=MIDDLE  ALT=\"%28r%2Bx%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B5%29%5E2 ALIGN=MIDDLE  ALT=\"%28r%2B5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. FOIL this expression out to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B5%29%5E2=r%5E2%2B10r%2B25 ALIGN=MIDDLE  ALT=\"%28r%2B5%29%5E2=r%5E2%2B10r%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we see that the value of k is k=25.\r<BR>\n" );
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document.write( "Hopefully you understand this whole process (if not, just ask). Once you do, there is a handy shortcut. The value of 'k' is simply equal to half the coefficient of 'r' squared. In other words,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%2810%2F2%29%5E2=5%5E2=25 ALIGN=MIDDLE  ALT=\"k=%2810%2F2%29%5E2=5%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is what we just got.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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