document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189934>Question 189934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello.<BR>\n" );
document.write( "Use completing the square to solve each equation:\r<BR>\n" );
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document.write( "-2 = 2x^2 - 5x\r<BR>\n" );
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document.write( "thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142509 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=142509\">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=-2+=+2x%5E2+-+5x+ ALIGN=MIDDLE  ALT=\"-2+=+2x%5E2+-+5x+\"   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=0+=+2x%5E2+-+5x+%2B2+ ALIGN=MIDDLE  ALT=\"0+=+2x%5E2+-+5x+%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+5x+%2B2+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+5x+%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-%285%2F2%29x%2B1%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-%285%2F2%29x%2B1%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=2 ALIGN=MIDDLE  ALT=\"2\"   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=-5%2F2 ALIGN=MIDDLE  ALT=\"-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4 ALIGN=MIDDLE  ALT=\"-5%2F4\"   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%28-5%2F2%29=-5%2F4 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28-5%2F2%29=-5%2F4\"   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=-5%2F4 ALIGN=MIDDLE  ALT=\"-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F16 ALIGN=MIDDLE  ALT=\"25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2F4%29%5E2=%28-5%2F4%29%28-5%2F4%29=25%2F16 ALIGN=MIDDLE  ALT=\"%28-5%2F4%29%5E2=%28-5%2F4%29%28-5%2F4%29=25%2F16\"   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-%285%2F2%29x%2Bhighlight%2825%2F16-25%2F16%29%2B1%29 ALIGN=MIDDLE  ALT=\"2%28x%5E2-%285%2F2%29x%2Bhighlight%2825%2F16-25%2F16%29%2B1%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=25%2F16 ALIGN=MIDDLE  ALT=\"25%2F16\"   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=25%2F16-25%2F16=0 ALIGN=MIDDLE  ALT=\"25%2F16-25%2F16=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=2%28%28x%5E2-%285%2F2%29x%2B25%2F16%29-25%2F16%2B1%29 ALIGN=MIDDLE  ALT=\"2%28%28x%5E2-%285%2F2%29x%2B25%2F16%29-25%2F16%2B1%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=2%28%28x-5%2F4%29%5E2-25%2F16%2B1%29 ALIGN=MIDDLE  ALT=\"2%28%28x-5%2F4%29%5E2-25%2F16%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%285%2F2%29x%2B25%2F16 ALIGN=MIDDLE  ALT=\"x%5E2-%285%2F2%29x%2B25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%2F4%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%28%28x-5%2F4%29%5E2-9%2F16%29 ALIGN=MIDDLE  ALT=\"2%28%28x-5%2F4%29%5E2-9%2F16%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=2%28x-5%2F4%29%5E2%2B2%28-9%2F16%29 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2%2B2%28-9%2F16%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=2%28x-5%2F4%29%5E2-9%2F8 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2-9%2F8\"   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=2x%5E2-5x%2B2 ALIGN=MIDDLE  ALT=\"2x%5E2-5x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-5%2F4%29%5E2-9%2F8 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2-9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-5x%2B2=2%28x-5%2F4%29%5E2-9%2F8 ALIGN=MIDDLE  ALT=\"2x%5E2-5x%2B2=2%28x-5%2F4%29%5E2-9%2F8\"   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=2x%5E2-5x%2B2=0 ALIGN=MIDDLE  ALT=\"2x%5E2-5x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-5%2F4%29%5E2-9%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2-9%2F8=0\"   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-5%2F4%29%5E2-9%2F8=0 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2-9%2F8=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=2%28x-5%2F4%29%5E2=0%2B9%2F8 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2=0%2B9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F8 ALIGN=MIDDLE  ALT=\"9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-5%2F4%29%5E2=9%2F8 ALIGN=MIDDLE  ALT=\"2%28x-5%2F4%29%5E2=9%2F8\"   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=%28x-5%2F4%29%5E2=%289%2F8%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%28x-5%2F4%29%5E2=%289%2F8%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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-5%2F4%29%5E2=9%2F16 ALIGN=MIDDLE  ALT=\"%28x-5%2F4%29%5E2=9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2F4=%22%22%2B-sqrt%289%2F16%29 ALIGN=MIDDLE  ALT=\"x-5%2F4=%22%22%2B-sqrt%289%2F16%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-5%2F4=sqrt%289%2F16%29 ALIGN=MIDDLE  ALT=\"x-5%2F4=sqrt%289%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2F4=-sqrt%289%2F16%29 ALIGN=MIDDLE  ALT=\"x-5%2F4=-sqrt%289%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the \"plus/minus\" to form two equations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2F4=3%2F4 ALIGN=MIDDLE  ALT=\"x-5%2F4=3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5%2F4=-3%2F4 ALIGN=MIDDLE  ALT=\"x-5%2F4=-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F16 ALIGN=MIDDLE  ALT=\"9%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   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=5%2F4%2B3%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4%2B3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F4-3%2F4 ALIGN=MIDDLE  ALT=\"x=5%2F4-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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