document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86176>Question 86176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help with this equation?<BR>\n" );
document.write( "Find the roots of 3x^2+2x-4=0.<BR>\n" );
document.write( "Thank you so much for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62263 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=62263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with the general quadratic\r<BR>\n" );
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document.write( "the general form of the quadratic equation is:\r<BR>\n" );
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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" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B2%2Ax-4 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B2%2Ax-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A3%2A-4+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=3, b=2, and c=-4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+4-4%2A3%2A-4+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4-4%2A3%2A-4+%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 2 to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+4%2B48+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4%2B48+%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-4%2A3 ALIGN=MIDDLE  ALT=\"-4%2A-4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+52+%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+52+%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 3 to get 6\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B+2%2Asqrt%2813%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B+2%2Asqrt%2813%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+-+2%2Asqrt%2813%29%29%2F6 ALIGN=MIDDLE  ALT=\"x+=+%28-2+-+2%2Asqrt%2813%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.86851709182133 ALIGN=MIDDLE  ALT=\"x=0.86851709182133\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.535183758488 ALIGN=MIDDLE  ALT=\"x=-1.535183758488\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.86851709182133 ALIGN=MIDDLE  ALT=\"x=0.86851709182133\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.535183758488 ALIGN=MIDDLE  ALT=\"x=-1.535183758488\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Ax%5E2%2B2%2Ax-4 ALIGN=MIDDLE  ALT=\"3%2Ax%5E2%2B2%2Ax-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-11.535183758488%2C+10.8685170918213%2C+-11.535183758488%2C+10.8685170918213%2C3%2Ax%5E2%2B2%2Ax%2B-4%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when we use the root finder feature on our calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.86851709182133 ALIGN=MIDDLE  ALT=\"x=0.86851709182133\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.535183758488 ALIGN=MIDDLE  ALT=\"x=-1.535183758488\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer<BR>\n" );
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