document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106099>Question 106099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by completing the square. Give exact Solutions.  <BR>\n" );
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document.write( "                        x^2 + 4x - 21 = 0\r<BR>\n" );
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document.write( "        ( X Squared plus four x Subtract twenty one equals zero.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77194 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To complete the square you want to come to an equation that looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you expand that form and look for common terms in your equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing with your equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2ax%2Ba%5E2=x%5E2%2B4x-21%2BZ ALIGN=MIDDLE  ALT=\"x%5E2%2B2ax%2Ba%5E2=x%5E2%2B4x-21%2BZ\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where Z is the constant I will add to both sides of my original equation to complete the square. <BR>\n" );
document.write( "Comparing the x term,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ax=4x ALIGN=MIDDLE  ALT=\"2ax=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=4 ALIGN=MIDDLE  ALT=\"2a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing my constant terms,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=-21%2BZ ALIGN=MIDDLE  ALT=\"a%5E2=-21%2BZ\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=-21%2BZ ALIGN=MIDDLE  ALT=\"4=-21%2BZ\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Z=25 ALIGN=MIDDLE  ALT=\"Z=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going back to the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+21+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add Z to both sides,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-21%2B25=+25 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-21%2B25=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B4=+25 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B4=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2=+25 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=5%29 ALIGN=MIDDLE  ALT=\"x%2B2=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=+-5 ALIGN=MIDDLE  ALT=\"x%2B2=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=5%29 ALIGN=MIDDLE  ALT=\"x%2B2=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=+-5 ALIGN=MIDDLE  ALT=\"x%2B2=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-7%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Always check your answers.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+21+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+%2B+4%283%29+-+21+=+0 ALIGN=MIDDLE  ALT=\"3%5E2+%2B+4%283%29+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B12-21=0 ALIGN=MIDDLE  ALT=\"9%2B12-21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Good answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+21+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%29%5E2+%2B+4%28-7%29+-+21+=+0 ALIGN=MIDDLE  ALT=\"%28-7%29%5E2+%2B+4%28-7%29+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49-28-21=0 ALIGN=MIDDLE  ALT=\"49-28-21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Good answer. <BR>\n" );
document.write( "x=3 and x=-7. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );