document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201572>Question 201572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve equation by completing the square<BR>\n" );
document.write( "n^2+16n-97=-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151793 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=151793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-97=-3 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-97=-3\"   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=n%5E2%2B16n-97%2B3=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-97%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Now let's complete the square for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94\"   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%2B16n-94 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Take half of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2816%29=8 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2816%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%5E2=%288%29%288%29=64 ALIGN=MIDDLE  ALT=\"%288%29%5E2=%288%29%288%29=64\"   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%2B16n%2Bhighlight%2864-64%29-94 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n%2Bhighlight%2864-64%29-94\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <font size=4><b>and</b></font> subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Make sure to place this after the \"n\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64-64=0 ALIGN=MIDDLE  ALT=\"64-64=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the expression is not changed.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2%2B16n%2B64%29-64-94 ALIGN=MIDDLE  ALT=\"%28n%5E2%2B16n%2B64%29-64-94\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the first three terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%5E2-64-94 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2-64-94\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n%2B64 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2\"   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=%28n%2B8%29%5E2-158 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2-158\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So after completing the square, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%5E2-158 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2-158\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94=%28n%2B8%29%5E2-158 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94=%28n%2B8%29%5E2-158\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%5E2-158=0 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2-158=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let's solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B16n-94=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B16n-94=0\"   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=%28n%2B8%29%5E2-158=0 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2-158=0\"   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=%28n%2B8%29%5E2=0%2B158 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2=0%2B158\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=158 ALIGN=MIDDLE  ALT=\"158\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B8%29%5E2=158 ALIGN=MIDDLE  ALT=\"%28n%2B8%29%5E2=158\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=%22%22%2B-sqrt%28158%29 ALIGN=MIDDLE  ALT=\"x%2B8=%22%22%2B-sqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B8=sqrt%28158%29 ALIGN=MIDDLE  ALT=\"n%2B8=sqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B8=-sqrt%28158%29 ALIGN=MIDDLE  ALT=\"n%2B8=-sqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the \"plus/minus\" to form two equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-8%2Bsqrt%28158%29 ALIGN=MIDDLE  ALT=\"n=-8%2Bsqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-8-sqrt%28158%29 ALIGN=MIDDLE  ALT=\"n=-8-sqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-8%2Bsqrt%28158%29 ALIGN=MIDDLE  ALT=\"n=-8%2Bsqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=-8-sqrt%28158%29 ALIGN=MIDDLE  ALT=\"n=-8-sqrt%28158%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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