document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169895>Question 169895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help show me how to work this problem out..Thank you...\r<BR>\n" );
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document.write( "solve equation using the quadratic formula\r<BR>\n" );
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document.write( "1/3x^2 + 2/9x - 1 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125321 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=125321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x%5E2+%2B+%282%2F9%29x+-+1+=+0 ALIGN=MIDDLE  ALT=\"%281%2F3%29x%5E2+%2B+%282%2F9%29x+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "quadratic formula is x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "standard form of the quadratic equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you can make your calculations easier by multiplying each side of the equation by 9.<BR>\n" );
document.write( "this will remove the denominators.<BR>\n" );
document.write( "since the right side of the equation was 0, it will remain 0.<BR>\n" );
document.write( "doing that, your formula becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+2x+-+9+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+2x+-+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "comparing to the standard form, you get<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "c = -9<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plugging these values into the quadratic formula, you get:<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%282%29+%2B-+root%282%2C%282%29%5E2-4%2A%283%29%2A%28-9%29%29%29%2F%282%2A%283%29%29 ALIGN=MIDDLE  ALT=\"%28-%282%29+%2B-+root%282%2C%282%29%5E2-4%2A%283%29%2A%28-9%29%29%29%2F%282%2A%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "x = 1.430500874<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = -2.097167541<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "plugging these values into your original equations proves these values are good if the equation stays true.<BR>\n" );
document.write( "it does.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "-----<BR>\n" );
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document.write( "it is much easier to see if you have an equation that factors easily.<BR>\n" );
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document.write( "take (x-1)*(x+2) = 0<BR>\n" );
document.write( "these factors are chosen so that the resulting equation factors easier when using the quadratic equation to solve it.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the resulting equation becomes x^2 +x-2=0<BR>\n" );
document.write( "use the quadratic formula to solve this:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = -2<BR>\n" );
document.write( "quadratic formula of x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B-+root%282%2Cb%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "becomes: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%281%29+%2B-+root%282%2C%281%29%5E2-4%2A%281%29%2A%28-2%29%29%29%2F%282%2A%281%29%29 ALIGN=MIDDLE  ALT=\"%28-%281%29+%2B-+root%282%2C%281%29%5E2-4%2A%281%29%2A%28-2%29%29%29%2F%282%2A%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this becomes: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%281%29+%2B-+root%282%2C9%29%29%2F%282%2A%281%29%29 ALIGN=MIDDLE  ALT=\"%28-%281%29+%2B-+root%282%2C9%29%29%2F%282%2A%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%281%29+%2B-+3%29%2F%282%29 ALIGN=MIDDLE  ALT=\"%28-%281%29+%2B-+3%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x = (-1+3)/2 = 1<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "x = (-1-3)/2 = -2<BR>\n" );
document.write( "if x = 1, then (x-1) = 0<BR>\n" );
document.write( "if x = -2, then (x+2) = 0<BR>\n" );
document.write( "these are the factors you started with in creating this problem so the answers come out good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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