document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969636>Question 969636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im trying to find the quadratic inequality of 3x^2 + 9x <= 4\r<BR>\n" );
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document.write( "Can somebody please explain step by step how to find the answer. The two things I seem to be confused by the most is the \"3x^2\" part because I'm used to problems that start with just \"x^2\" and the \"<=\". Any help would be highly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592463 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=592463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Put into general form, and either factor if possible, or use general solution for finding roots or quadratic expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B9x-4%3C=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B9x-4%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Try search for factorability:<BR>\n" );
document.write( "(3x  2)(x  2)------2x and 3x------not useful.<BR>\n" );
document.write( "(3x  1)(x   4)-------1x and 12x-----no useful.<BR>\n" );
document.write( "(3x   4)(x   1 )-----4x and 3x------no use.<BR>\n" );
document.write( "The quadratic expression is not factorable with simple integers.\r<BR>\n" );
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document.write( "Check discriminant:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%5E2%29-4%2A3%2A%28-4%29 ALIGN=MIDDLE  ALT=\"%289%5E2%29-4%2A3%2A%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2B16 ALIGN=MIDDLE  ALT=\"81%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=97 ALIGN=MIDDLE  ALT=\"97\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Roots are the critical values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9-+sqrt%2897%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28-9-+sqrt%2897%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >   and   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%2B+sqrt%2897%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28-9%2B+sqrt%2897%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can check the three intervals of the x-axis to determine where is the solution.  Pick any single value in each of these intervals:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=%28-9-sqrt%2897%29%29%2F6 ALIGN=MIDDLE  ALT=\"x%3C=%28-9-sqrt%2897%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9-sqrt%2897%29%29%2F6%3C=x%3C=%28-9%2Bsqrt%2897%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28-9-sqrt%2897%29%29%2F6%3C=x%3C=%28-9%2Bsqrt%2897%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9%2Bsqrt%2897%29%29%2F6%3C=x ALIGN=MIDDLE  ALT=\"%28-9%2Bsqrt%2897%29%29%2F6%3C=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The exercise must be in the intermediate level because the quadratic part is not factorable and needs the general solution of finding roots for a quadratic expression for defining intervals.  No way trying to avoid starting with \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"  or what \"<=\" means. </SPAN>\n" );
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