document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103658>Question 103658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by completing the square.  	2x^2 – 6x – 3 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75530 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=75530\">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=2x%5E2-6x-3=0 ALIGN=MIDDLE  ALT=\"2x%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=2x%5E2-6x=3 ALIGN=MIDDLE  ALT=\"2x%5E2-6x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-3x%29=3 ALIGN=MIDDLE  ALT=\"2%28x%5E2-3x%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading coefficient 2.  This step is important since we want 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 to be equal to 1.\r<BR>\n" );
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document.write( "Take half of the x coefficient -3 to get -1.5 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2=-1.5 ALIGN=MIDDLE  ALT=\"-3%2F2=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Now square -1.5 to get 2.25 (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.5%29%5E2=2.25 ALIGN=MIDDLE  ALT=\"%28-1.5%29%5E2=2.25\"   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=2%28x%5E2-3x%2B2.25%29=3%2B2.25%282%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-3x%2B2.25%29=3%2B2.25%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add this result (2.25) to the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x ALIGN=MIDDLE  ALT=\"x%5E2-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  inside the parenthesis. Now the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B2.25 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a perfect square trinomial. Now add the result (2.25)(2) (remember we factored out a 2) to the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-1.5%29%5E2=3%2B2.25%282%29 ALIGN=MIDDLE  ALT=\"2%28x-1.5%29%5E2=3%2B2.25%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B2.25 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1.5%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1.5%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=2%28x-1.5%29%5E2=3%2B4.5 ALIGN=MIDDLE  ALT=\"2%28x-1.5%29%5E2=3%2B4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2.25 and 2 to get 4.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-1.5%29%5E2=7.5 ALIGN=MIDDLE  ALT=\"2%28x-1.5%29%5E2=7.5\"   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=%28x-1.5%29%5E2=3.75 ALIGN=MIDDLE  ALT=\"%28x-1.5%29%5E2=3.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1.5=0%2B-sqrt%283.75%29 ALIGN=MIDDLE  ALT=\"x-1.5=0%2B-sqrt%283.75%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=1.5%2B-sqrt%283.75%29 ALIGN=MIDDLE  ALT=\"x=1.5%2B-sqrt%283.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1.5 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=1.5%2Bsqrt%283.75%29 ALIGN=MIDDLE  ALT=\"x=1.5%2Bsqrt%283.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.5-sqrt%283.75%29 ALIGN=MIDDLE  ALT=\"x=1.5-sqrt%283.75%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=3.43649167310371 ALIGN=MIDDLE  ALT=\"x=3.43649167310371\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.436491673103709 ALIGN=MIDDLE  ALT=\"x=-0.436491673103709\"   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+2x%5E2-6x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%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=2x%5E2-6x-3 ALIGN=MIDDLE  ALT=\"y=2x%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=3.43649167310371 ALIGN=MIDDLE  ALT=\"x=3.43649167310371\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-0.436491673103709 ALIGN=MIDDLE  ALT=\"x=-0.436491673103709\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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