document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123070>Question 123070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve for x: 3x^2+4x-9=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90334 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=90334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's use the quadratic formula to solve for x:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B4%2Ax-9=0 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B4%2Ax-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-9 ALIGN=MIDDLE  ALT=\"c=-9\"   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=x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A3%2A-9+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A3%2A-9+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=4, and c=-9\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=x+=+%28-4+%2B-+sqrt%28+16-4%2A3%2A-9+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16-4%2A3%2A-9+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16  \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=x+=+%28-4+%2B-+sqrt%28+16%2B108+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16%2B108+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-9%2A3 ALIGN=MIDDLE  ALT=\"-4%2A-9%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108 ALIGN=MIDDLE  ALT=\"108\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=x+=+%28-4+%2B-+sqrt%28+124+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+124+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\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=x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\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=x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So now the expression breaks down into two parts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+2%2Asqrt%2831%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+2%2Asqrt%2831%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+2%2Asqrt%2831%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+2%2Asqrt%2831%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now break up the fraction\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=x=-4%2F6%2B2%2Asqrt%2831%29%2F6 ALIGN=MIDDLE  ALT=\"x=-4%2F6%2B2%2Asqrt%2831%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2F6-2%2Asqrt%2831%29%2F6 ALIGN=MIDDLE  ALT=\"x=-4%2F6-2%2Asqrt%2831%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "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/plot-formula.mpl?expression=x=-2+%2F+3%2Bsqrt%2831%29%2F3 ALIGN=MIDDLE  ALT=\"x=-2+%2F+3%2Bsqrt%2831%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2+%2F+3-sqrt%2831%29%2F3 ALIGN=MIDDLE  ALT=\"x=-2+%2F+3-sqrt%2831%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So these expressions approximate to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.18925478761001 ALIGN=MIDDLE  ALT=\"x=1.18925478761001\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.52258812094334 ALIGN=MIDDLE  ALT=\"x=-2.52258812094334\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.18925478761001 ALIGN=MIDDLE  ALT=\"x=1.18925478761001\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.52258812094334 ALIGN=MIDDLE  ALT=\"x=-2.52258812094334\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B4%2Ax-9 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B4%2Ax-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-12.5225881209433%2C+11.18925478761%2C+-12.5225881209433%2C+11.18925478761%2C3%2Ax%5E2%2B4%2Ax%2B-9%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when we use the root finder feature on a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.18925478761001 ALIGN=MIDDLE  ALT=\"x=1.18925478761001\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.52258812094334 ALIGN=MIDDLE  ALT=\"x=-2.52258812094334\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );