document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=736993>Question 736993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Completing the Square\r<BR>\n" );
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document.write( "What is half of -4y/3 squared?\r<BR>\n" );
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document.write( "3y^2-4y-1=0\r<BR>\n" );
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document.write( "3y^2/3-4y/3-1/3=0/3\r<BR>\n" );
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document.write( "y^2-4y/3=1/3 This is where I get stuck.\r<BR>\n" );
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document.write( "I'm supposed to take half of -4y/3 and square it. \r<BR>\n" );
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document.write( "I'm not quite understanding how to do  it. Do you square both -4 and 3 separately? Then it becomes -16y/9?\r<BR>\n" );
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document.write( "If you halve it, it becomes -2y/1.5?? Should you not have a decimal or a fraction?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450083 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=450083\">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=+3y%5E2+-+4y+-+1+=+0+ ALIGN=MIDDLE  ALT=\"+3y%5E2+-+4y+-+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3y%5E2+-+4y+=+1+ ALIGN=MIDDLE  ALT=\"+3y%5E2+-+4y+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+%284%2F3%29%2Ay+=+1%2F3+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+%284%2F3%29%2Ay+=+1%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this equation,  which is for finding the roots,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is called the independent variable.<BR>\n" );
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document.write( "It would be plotted on the horizontal axis, <BR>\n" );
document.write( "which is normally 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;\" > axis.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The rule for completing the square is:<BR>\n" );
document.write( "Take 1/2 of the co-efficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "term ( usually called 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;\" > term  ),<BR>\n" );
document.write( "square it, then add it to both sides<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "The co-efficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-4%2F3%29+%2F+2+=+-4%2F6+ ALIGN=MIDDLE  ALT=\"+%28-4%2F3%29+%2F+2+=+-4%2F6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2F6+=+-2%2F3+ ALIGN=MIDDLE  ALT=\"+-4%2F6+=+-2%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now square it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%2F3+%29%5E2+=+4%2F9+ ALIGN=MIDDLE  ALT=\"+%28-2%2F3+%29%5E2+=+4%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add it to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+1%2F3+%2B+4%2F9+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+1%2F3+%2B+4%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+3%2F9+%2B+4%2F9+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+3%2F9+%2B+4%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+7%2F9+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+%284%2F3%29%2Ay++%2B+4%2F9+=+7%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+2%2F3+%29%5E2+=+%28+sqrt%287%29+%2F+3+%29%5E2+ ALIGN=MIDDLE  ALT=\"+%28+y+-+2%2F3+%29%5E2+=+%28+sqrt%287%29+%2F+3+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+-+2%2F3+=+sqrt%287%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+y+-+2%2F3+=+sqrt%287%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+2+%2B+sqrt%287%29+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+y+=+%28+2+%2B+sqrt%287%29+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28+2+-+sqrt%287%29+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+y+=+%28+2+-+sqrt%287%29+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Here's a plot of the entire equation, which can<BR>\n" );
document.write( "be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z+=+3y%5E2+-+4y+-+1+ ALIGN=MIDDLE  ALT=\"+z+=+3y%5E2+-+4y+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%287%29+=+2.6458+ ALIGN=MIDDLE  ALT=\"+sqrt%287%29+=+2.6458+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2+%2B+2.6458+%29+%2F+3+=+1.5486+ ALIGN=MIDDLE  ALT=\"+%28+2+%2B+2.6458+%29+%2F+3+=+1.5486+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2+-+2.6458+%29+%2F+3+=+-.2153+ ALIGN=MIDDLE  ALT=\"+%28+2+-+2.6458+%29+%2F+3+=+-.2153+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see that these are the horizontal axis crossings<BR>\n" );
document.write( "( Unless I messed up )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+6%2C+3x%5E2+-+4x+-+1+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+6%2C+3x%5E2+-+4x+-+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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