document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118450>Question 118450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need some help on finding the value of c that makes each trinomial a perfect square. The problem is;<BR>\n" );
document.write( "[n^2+14n+c]<BR>\n" );
document.write( "I have tried the formula: [(a+b)^2=a^2+2ab+b^2]<BR>\n" );
document.write( "But I seem to be getting stuck trying to find the value of [b]\r<BR>\n" );
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document.write( "May someone show me how to work out the problem?<BR>\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 #86566 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=86566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we're trying to make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2Bc ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > a perfect square, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=n%5E2%2B14n%2Bc ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=n%5E2%2B14n%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2=n%5E2%2B14n%2Bc ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2=n%5E2%2B14n%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil <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( "Since we know that the first term on the right is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=n%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=n ALIGN=MIDDLE  ALT=\"a=n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2nb%2Bb%5E2=n%5E2%2B14n%2Bc ALIGN=MIDDLE  ALT=\"n%5E2%2B2nb%2Bb%5E2=n%5E2%2B14n%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=n ALIGN=MIDDLE  ALT=\"a=n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2nb=14n ALIGN=MIDDLE  ALT=\"2nb=14n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how both of these terms only have 1 \"n\") and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=c ALIGN=MIDDLE  ALT=\"b%5E2=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice how both of these terms have no \"n\" terms)\r<BR>\n" );
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document.write( "So let's use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2nb=14n ALIGN=MIDDLE  ALT=\"2nb=14n\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for b\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2nb=14n ALIGN=MIDDLE  ALT=\"2nb=14n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282n%2F2n%29b=14n%2F2n ALIGN=MIDDLE  ALT=\"cross%282n%2F2n%29b=14n%2F2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2n to isolate b\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2B7%5E2 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2B7%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the original polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2Bc ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2B49 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now square 7 to get 49\r<BR>\n" );
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document.write( "So this means that the perfect square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2B49 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Notice how if we factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2B49 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B7%29%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B7%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B14n%2B49 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square. So our answer is verified. </SPAN>\n" );
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