document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196864>Question 196864</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937760/algebrahomeworkh>McDougal Littell Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: x^2+3/5x-1=0\r<BR>\n" );
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document.write( "It is called completing the square and has to do with solving quadratic equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147600 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=147600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's complete the square:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%283%2F5%29x-1 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283%2F5%29x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the left side of the given equation.\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=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   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%283%2F5%29=3%2F10 ALIGN=MIDDLE  ALT=\"%281%2F2%29%283%2F5%29=3%2F10\"   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=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F100 ALIGN=MIDDLE  ALT=\"9%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F10%29%5E2=%283%2F10%29%283%2F10%29=9%2F100 ALIGN=MIDDLE  ALT=\"%283%2F10%29%5E2=%283%2F10%29%283%2F10%29=9%2F100\"   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%2B%283%2F5%29x%2Bhighlight%289%2F100-9%2F100%29-1 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283%2F5%29x%2Bhighlight%289%2F100-9%2F100%29-1\"   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=9%2F100 ALIGN=MIDDLE  ALT=\"9%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Make sure to place this after the \"x\" term. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F100-9%2F100=0 ALIGN=MIDDLE  ALT=\"9%2F100-9%2F100=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=%28x%5E2%2B%283%2F5%29x%2B9%2F100%29-9%2F100-1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B%283%2F5%29x%2B9%2F100%29-9%2F100-1\"   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=%28x%2B3%2F10%29%5E2-9%2F100-1 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-9%2F100-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%283%2F5%29x%2B9%2F100 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283%2F5%29x%2B9%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F10%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%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=%28x%2B3%2F10%29%5E2-109%2F100 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-109%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\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=x%5E2%2B3%2F5x-1 ALIGN=MIDDLE  ALT=\"x%5E2%2B3%2F5x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > transforms to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F10%29%5E2-109%2F100 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-109%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3%2F5x-1=%28x%2B3%2F10%29%5E2-109%2F100 ALIGN=MIDDLE  ALT=\"x%5E2%2B3%2F5x-1=%28x%2B3%2F10%29%5E2-109%2F100\"   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=x%5E2%2B%283%2F5%29x-1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B%283%2F5%29x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F10%29%5E2-109%2F100=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-109%2F100=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( "Now let's solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%2F10%29%5E2-109%2F100=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-109%2F100=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=%28x%2B3%2F10%29%5E2-109%2F100=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2-109%2F100=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=%28x%2B3%2F10%29%5E2=0%2B109%2F100 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2=0%2B109%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=109%2F100 ALIGN=MIDDLE  ALT=\"109%2F100\"   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=%28x%2B3%2F10%29%5E2=109%2F100 ALIGN=MIDDLE  ALT=\"%28x%2B3%2F10%29%5E2=109%2F100\"   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=x%2B3%2F10=0%2B-sqrt%28109%2F100%29 ALIGN=MIDDLE  ALT=\"x%2B3%2F10=0%2B-sqrt%28109%2F100%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%2B3%2F10=sqrt%28109%2F100%29 ALIGN=MIDDLE  ALT=\"x%2B3%2F10=sqrt%28109%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F10=-sqrt%28109%2F100%29 ALIGN=MIDDLE  ALT=\"x%2B3%2F10=-sqrt%28109%2F100%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%2B3%2F10=sqrt%28109%29%2F10 ALIGN=MIDDLE  ALT=\"x%2B3%2F10=sqrt%28109%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3%2F10=-sqrt%28109%29%2F10 ALIGN=MIDDLE  ALT=\"x%2B3%2F10=-sqrt%28109%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Simplify the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F10%2Bsqrt%28109%29%2F10 ALIGN=MIDDLE  ALT=\"x=-3%2F10%2Bsqrt%28109%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F10-sqrt%28109%29%2F10 ALIGN=MIDDLE  ALT=\"x=-3%2F10-sqrt%28109%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F10 ALIGN=MIDDLE  ALT=\"3%2F10\"   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=x=%28-3%2Bsqrt%28109%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%28-3%2Bsqrt%28109%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-3-sqrt%28109%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%28-3-sqrt%28109%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\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=%28-3%2Bsqrt%28109%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%28-3%2Bsqrt%28109%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-3-sqrt%28109%29%29%2F%2810%29 ALIGN=MIDDLE  ALT=\"x=%28-3-sqrt%28109%29%29%2F%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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