document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93653>Question 93653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation algebraically.\r<BR>\n" );
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document.write( "2x-x^2-18x+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 #68226 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=68226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-x%5E2-18x%2B9=0 ALIGN=MIDDLE  ALT=\"2x-x%5E2-18x%2B9=0\"   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%5E2-16x%2B9=0 ALIGN=MIDDLE  ALT=\"-x%5E2-16x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "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=-x%5E2-16%2Ax%2B9=0 ALIGN=MIDDLE  ALT=\"-x%5E2-16%2Ax%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-16 ALIGN=MIDDLE  ALT=\"b=-16\"   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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--16+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=-16, and c=9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%2A-1%2A9+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -16 to get 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+%2B-+sqrt%28+256-4%2A-1%2A9+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256-4%2A-1%2A9+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -16 to get 256  (note: remember when you square -16, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%29%5E2=-16%2A-16=256 ALIGN=MIDDLE  ALT=\"%28-16%29%5E2=-16%2A-16=256\"   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+=+%2816+%2B-+sqrt%28+256%2B36+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+256%2B36+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A9%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A9%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   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+=+%2816+%2B-+sqrt%28+292+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+sqrt%28+292+%29%29%2F%282%2A-1%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+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F%282%2A-1%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+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B-+2%2Asqrt%2873%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2\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+=+%2816+%2B+2%2Asqrt%2873%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%2816+%2B+2%2Asqrt%2873%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2816+-+2%2Asqrt%2873%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x+=+%2816+-+2%2Asqrt%2873%29%29%2F-2\"   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=%2B16%2F-2%2B2%2Asqrt%2873%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%2B16%2F-2%2B2%2Asqrt%2873%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B16%2F-2-2%2Asqrt%2873%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%2B16%2F-2-2%2Asqrt%2873%29%2F-2\"   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=-8-sqrt%2873%29 ALIGN=MIDDLE  ALT=\"x=-8-sqrt%2873%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8%2Bsqrt%2873%29 ALIGN=MIDDLE  ALT=\"x=-8%2Bsqrt%2873%29\"   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=-16.5440037453175 ALIGN=MIDDLE  ALT=\"x=-16.5440037453175\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.54400374531753 ALIGN=MIDDLE  ALT=\"x=0.54400374531753\"   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( "Notice when we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-16%2Ax%2B9 ALIGN=MIDDLE  ALT=\"-x%5E2-16%2Ax%2B9\"   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+-26.5440037453175%2C+10.5440037453175%2C+-26.5440037453175%2C+10.5440037453175%2C-1%2Ax%5E2%2B-16%2Ax%2B9%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=-16.5440037453175 ALIGN=MIDDLE  ALT=\"x=-16.5440037453175\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.54400374531753 ALIGN=MIDDLE  ALT=\"x=0.54400374531753\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So this verifies our answer </SPAN>\n" );
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