document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165592>Question 165592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, If 3x^2-2x+7=0, then (x-1/3)^2=\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122084 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=122084\">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=3x%5E2-2x%2B7 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-%282%2F3%29x%2B7%2F3%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2-%282%2F3%29x%2B7%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This step is very important: the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <font size=4><b>must</b></font> be equal to 1.\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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   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%28-2%2F3%29=-1%2F3 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-2%2F3%29=-1%2F3\"   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=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29%5E2=%28-1%2F3%29%28-1%2F3%29=1%2F9 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29%5E2=%28-1%2F3%29%28-1%2F3%29=1%2F9\"   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=3%28x%5E2-%282%2F3%29x%2Bhighlight%281%2F9-1%2F9%29%2B7%2F3%29 ALIGN=MIDDLE  ALT=\"3%28x%5E2-%282%2F3%29x%2Bhighlight%281%2F9-1%2F9%29%2B7%2F3%29\"   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=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > inside the parenthesis. Make sure to place this after the \"x\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9-1%2F9=0 ALIGN=MIDDLE  ALT=\"1%2F9-1%2F9=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=3%28%28x%5E2-%282%2F3%29x%2B1%2F9%29-1%2F9%2B7%2F3%29 ALIGN=MIDDLE  ALT=\"3%28%28x%5E2-%282%2F3%29x%2B1%2F9%29-1%2F9%2B7%2F3%29\"   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=3%28%28x-1%2F3%29%5E2-1%2F9%2B7%2F3%29 ALIGN=MIDDLE  ALT=\"3%28%28x-1%2F3%29%5E2-1%2F9%2B7%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%282%2F3%29x%2B1%2F9 ALIGN=MIDDLE  ALT=\"x%5E2-%282%2F3%29x%2B1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%2F3%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=3%28%28x-1%2F3%29%5E2%2B20%2F9%29 ALIGN=MIDDLE  ALT=\"3%28%28x-1%2F3%29%5E2%2B20%2F9%29\"   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=3%28x-1%2F3%29%5E2%2B3%2820%2F9%29 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2%2B3%2820%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%2F3%29%5E2%2B20%2F3 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2%2B20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\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=3x%5E2-2x%2B7 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%2F3%29%5E2%2B20%2F3 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2%2B20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x%2B7=3%28x-1%2F3%29%5E2%2B20%2F3 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2B7=3%28x-1%2F3%29%5E2%2B20%2F3\"   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=3x%5E2-2x%2B7=0 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2B7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%2F3%29%5E2%2B20%2F3=0 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2%2B20%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "----------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%2F3%29%5E2%2B20%2F3=0 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2%2B20%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation (this equation is the same as the original equation)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-1%2F3%29%5E2=-20%2F3 ALIGN=MIDDLE  ALT=\"3%28x-1%2F3%29%5E2=-20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F3 ALIGN=MIDDLE  ALT=\"20%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fcross%283%29%29%28cross%283%29%29%28x-1%2F3%29%5E2=%28-20%2F3%29%281%2F3%29 ALIGN=MIDDLE  ALT=\"%281%2Fcross%283%29%29%28cross%283%29%29%28x-1%2F3%29%5E2=%28-20%2F3%29%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   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=%28x-1%2F3%29%5E2=-20%2F9 ALIGN=MIDDLE  ALT=\"%28x-1%2F3%29%5E2=-20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2F3%29%5E2=-20%2F9 ALIGN=MIDDLE  ALT=\"%28x-1%2F3%29%5E2=-20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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