document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=94356>Question 94356</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the problem is:<BR>\n" );
document.write( "-3x(squared)+6x+23=0\r<BR>\n" );
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document.write( "I understand how to do the formula, but when I try to get my answers for x, they are different then the answer on the answer sheet. Can you break down the problem for me please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68713 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=68713\">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" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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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" );
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document.write( "the general solution using 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%2B6%2Ax%2B23=0 ALIGN=MIDDLE  ALT=\"-3%2Ax%5E2%2B6%2Ax%2B23=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=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=23 ALIGN=MIDDLE  ALT=\"c=23\"   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+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A-3%2A23+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A-3%2A23+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-3, b=6, and c=23\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+36-4%2A-3%2A23+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36-4%2A-3%2A23+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 6 to get 36  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+sqrt%28+36%2B276+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+36%2B276+%29%29%2F%282%2A-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A23%2A-3 ALIGN=MIDDLE  ALT=\"-4%2A23%2A-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=276 ALIGN=MIDDLE  ALT=\"276\"   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+=+%28-6+%2B-+sqrt%28+312+%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+sqrt%28+312+%29%29%2F%282%2A-3%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+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F%282%2A-3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F%282%2A-3%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B-+2%2Asqrt%2878%29%29%2F-6\"   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+=+%28-6+%2B+2%2Asqrt%2878%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+%2B+2%2Asqrt%2878%29%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-6+-+2%2Asqrt%2878%29%29%2F-6 ALIGN=MIDDLE  ALT=\"x+=+%28-6+-+2%2Asqrt%2878%29%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6%2F-6%2B2%2Asqrt%2878%29%2F-6 ALIGN=MIDDLE  ALT=\"x=-6%2F-6%2B2%2Asqrt%2878%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6%2F-6-2%2Asqrt%2878%29%2F-6 ALIGN=MIDDLE  ALT=\"x=-6%2F-6-2%2Asqrt%2878%29%2F-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1-sqrt%2878%29%2F3 ALIGN=MIDDLE  ALT=\"x=1-sqrt%2878%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%2878%29%2F3 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%2878%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.94392028877595 ALIGN=MIDDLE  ALT=\"x=-1.94392028877595\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.94392028877595 ALIGN=MIDDLE  ALT=\"x=3.94392028877595\"   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=-1.94392028877595 ALIGN=MIDDLE  ALT=\"x=-1.94392028877595\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.94392028877595 ALIGN=MIDDLE  ALT=\"x=3.94392028877595\"   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%2B6%2Ax%2B23 ALIGN=MIDDLE  ALT=\"-3%2Ax%5E2%2B6%2Ax%2B23\"   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+-11.9439202887759%2C+13.9439202887759%2C+-11.9439202887759%2C+13.9439202887759%2C-3%2Ax%5E2%2B6%2Ax%2B23%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 a calculator, we find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1.94392028877595 ALIGN=MIDDLE  ALT=\"x=-1.94392028877595\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.94392028877595 ALIGN=MIDDLE  ALT=\"x=3.94392028877595\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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