document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1912>Question 1912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square.\r<BR>\n" );
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document.write( "z^2 + z = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to write the lefthand side as a \"square\" eg <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"%28z%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we need to figure out what is missing and add it in, so the standard square is as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ba%29%5E2+=+x%5E2+%2B+2ax+%2B+a%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Ba%29%5E2+=+x%5E2+%2B+2ax+%2B+a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, we would need to find the number \"a\"...so look at the coefficient of the x-term. You have 1z so 2a is equivalent to 1 therefore a itself must be 1/2. If that is so, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be 1/4.\r<BR>\n" );
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document.write( "so, we would need to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+%2B+z+%2B+%281%2F4%29 ALIGN=MIDDLE  ALT=\"z%5E2+%2B+z+%2B+%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but we cannot JUST add a 1/4 to one side...we need to add it to both sides, to keep the equation \"unchanged\", so we actually get the following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+%2B+z+%2B+%281%2F4%29+=+2+%2B+%281%2F4%29 ALIGN=MIDDLE  ALT=\"z%5E2+%2B+z+%2B+%281%2F4%29+=+2+%2B+%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B%281%2F2%29%29%5E2+=+%289%2F4%29 ALIGN=MIDDLE  ALT=\"%28z%2B%281%2F2%29%29%5E2+=+%289%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so now, taking square root of both sides, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B%281%2F2%29 ALIGN=MIDDLE  ALT=\"z%2B%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29 ALIGN=MIDDLE  ALT=\"%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....ALWAYS remember the +- when square rooting!!!!\r<BR>\n" );
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document.write( "so z+1/2 = 3/2 or z+1/2 = -3/2\r<BR>\n" );
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document.write( "so z=1, or z=-2\r<BR>\n" );
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document.write( "Make sense?\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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