document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93435>Question 93435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the quadratic equation by completing the square.\r<BR>\n" );
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document.write( "x^2-6x-3=0\r<BR>\n" );
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document.write( "Can you help me with this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68032 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=68032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x-3=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x-3=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=x%5E2-6x=3 ALIGN=MIDDLE  ALT=\"x%5E2-6x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides\r<BR>\n" );
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document.write( "Take half of the x coefficient -6 to get -3 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2F2=-3 ALIGN=MIDDLE  ALT=\"-6%2F2=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square -3 to get 9 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2=9\"   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=x%5E2-6x%2B9=3%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=3%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (9) to both sides. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfect square trinomial.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=3%2B9 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=3%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (note: if you need help with factoring, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2=12 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0%2B-sqrt%2812%29 ALIGN=MIDDLE  ALT=\"x-3=0%2B-sqrt%2812%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=x=3%2B-sqrt%2812%29 ALIGN=MIDDLE  ALT=\"x=3%2B-sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides to isolate x.\r<BR>\n" );
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document.write( "So the expression breaks down to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2Bsqrt%2812%29 ALIGN=MIDDLE  ALT=\"x=3%2Bsqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3-sqrt%2812%29 ALIGN=MIDDLE  ALT=\"x=3-sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our answer is approximately\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.46410161513775 ALIGN=MIDDLE  ALT=\"x=6.46410161513775\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.464101615137754 ALIGN=MIDDLE  ALT=\"x=-0.464101615137754\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is visual proof\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-6x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-6x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-6x-3 ALIGN=MIDDLE  ALT=\"y=x%5E2-6x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When we use the root finder feature on a calculator, we would find that the x-intercepts are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6.46410161513775 ALIGN=MIDDLE  ALT=\"x=6.46410161513775\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.464101615137754 ALIGN=MIDDLE  ALT=\"x=-0.464101615137754\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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