document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=134329>Question 134329</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073348147/algebrahomeworkh>beginning algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x%5E2%2B5x-1=0+ ALIGN=MIDDLE  ALT=\"+3x%5E2%2B5x-1=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Please help me solve this equation by completing the square  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #98241 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=98241\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+x%5E2%2B5+x-1=0 ALIGN=MIDDLE  ALT=\"3+x%5E2%2B5+x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+x%5E2%2B5+x=1 ALIGN=MIDDLE  ALT=\"3+x%5E2%2B5+x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2%2B%285%2F3%29x%29=1 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B%285%2F3%29x%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the leading 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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take half of the x coefficient <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%285%2F3%29=5%2F6 ALIGN=MIDDLE  ALT=\"%281%2F2%29%285%2F3%29=5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F36 ALIGN=MIDDLE  ALT=\"25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29%5E2=%285%2F6%29%285%2F6%29=25%2F36 ALIGN=MIDDLE  ALT=\"%285%2F6%29%5E2=%285%2F6%29%285%2F6%29=25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2%2B%285%2F3%29x%2B25%2F36-25%2F36%29=1 ALIGN=MIDDLE  ALT=\"3%28x%5E2%2B%285%2F3%29x%2B25%2F36-25%2F36%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F36 ALIGN=MIDDLE  ALT=\"25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not change the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%28x%2B5%2F6%29%5E2-25%2F36%29=1 ALIGN=MIDDLE  ALT=\"3%28%28x%2B5%2F6%29%5E2-25%2F36%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%285%2F3%29x%2B25%2F36 ALIGN=MIDDLE  ALT=\"x%5E2%2B%285%2F3%29x%2B25%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B5%2F6%29%5E2-3%2825%2F36%29=1 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F6%29%5E2-3%2825%2F36%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B5%2F6%29%5E2-25%2F12=1 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F6%29%5E2-25%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B5%2F6%29%5E2-25%2F12-1=1 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F6%29%5E2-25%2F12-1=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1 ALIGN=MIDDLE  ALT=\"%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to isolate y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B5%2F6%29%5E2-37%2F12=1 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F6%29%5E2-37%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2B5%2F6%29%5E2=%2B37%2F12 ALIGN=MIDDLE  ALT=\"3%28x%2B5%2F6%29%5E2=%2B37%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F12 ALIGN=MIDDLE  ALT=\"37%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F6%29%5E2=%2837%2F12%29%2F%283%29 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F6%29%5E2=%2837%2F12%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%2F6%29%5E2=37%2F36 ALIGN=MIDDLE  ALT=\"%28x%2B5%2F6%29%5E2=37%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x+\frac{5}{6}=\pm \sqrt{\frac{37}{36}}\"> Take the square root of both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x+\frac{5}{6}=\pm \frac{\sqrt{37}}{6}\"> Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x=-\frac{5}{6}\pm \frac{\sqrt{37}}{6}\">  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x= \frac{-5\pm\sqrt{37}}{6}\">  Combine the fractions\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our solutions are \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x= \frac{-5+\sqrt{37}}{6}\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x= \frac{-5-\sqrt{37}}{6}\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );