document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123486>Question 123486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John used completing the square to find the zeros of the function          y=9x^2-12x-33. Can someone please show please show me the steps for solving this ??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90733 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> John used completing the square to find the zeros of the function <BR>\n" );
document.write( "y = 9x^2 - 12x - 33<BR>\n" );
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document.write( "Find the zeros:<BR>\n" );
document.write( "9y^2 - 12x - 33 = 0<BR>\n" );
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document.write( "When completing the square, y^2 has to have a coefficient of 1, <BR>\n" );
document.write( "divide each term by 9:<BR>\n" );
document.write( "y^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2F9 ALIGN=MIDDLE  ALT=\"33%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
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document.write( "We are going to replace the 3rd term with a value that will make it a square<BR>\n" );
document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2F9 ALIGN=MIDDLE  ALT=\"33%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:<BR>\n" );
document.write( "y^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + ____  =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2F9 ALIGN=MIDDLE  ALT=\"33%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can determine the 3rd term as follows:<BR>\n" );
document.write( "Divide the coefficient of x by 2; that would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F9 ALIGN=MIDDLE  ALT=\"6%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square this value; that would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2F81 ALIGN=MIDDLE  ALT=\"36%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduced to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F9 ALIGN=MIDDLE  ALT=\"4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "y^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F9 ALIGN=MIDDLE  ALT=\"4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2F9 ALIGN=MIDDLE  ALT=\"33%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F9 ALIGN=MIDDLE  ALT=\"4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >; we have to add the same amt to both sides to keep an equation<BR>\n" );
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document.write( "y^2 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F9 ALIGN=MIDDLE  ALT=\"12%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F9 ALIGN=MIDDLE  ALT=\"4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F9 ALIGN=MIDDLE  ALT=\"37%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Now it is a square, and can be factored to:<BR>\n" );
document.write( "(y - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) (y - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F9 ALIGN=MIDDLE  ALT=\"37%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "(y - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=37%2F9 ALIGN=MIDDLE  ALT=\"37%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the square root of both sides and we have;<BR>\n" );
document.write( "y - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2837%2F9%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2837%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "y = +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2837%2F9%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2837%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > add 2/3 to both sides<BR>\n" );
document.write( "We can factor 1/3 out of the radical, gets rid of the denominator inside the radical<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29sqrt%2837%29%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29sqrt%2837%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+%2B+sqrt%2837%29%29%2F3 ALIGN=MIDDLE  ALT=\"%282+%2B+sqrt%2837%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+-+sqrt%2837%29%29%2F3 ALIGN=MIDDLE  ALT=\"%282+-+sqrt%2837%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "There are a lot of steps here. I hope you will take the time to study each one<BR>\n" );
document.write( "If you have any questions, you can email me.  Ankor<BR>\n" );
document.write( " </SPAN>\n" );
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