document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29300>Question 29300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 0 = 5(x^3) + 10 + 10(x^2)<BR>\n" );
document.write( "solve for x? or factor? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16142 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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/cgi-bin/show-face.mpl?user=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not too sure how to approach this apart from a numerical one... We have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2%2B2=0 ALIGN=MIDDLE  ALT=\"x%5E3%2B2x%5E2%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This does not factorise easily.\r<BR>\n" );
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document.write( "Approach is:<BR>\n" );
document.write( "pick value of x<BR>\n" );
document.write( "find the value of y<BR>\n" );
document.write( "pick another value of x<BR>\n" );
document.write( "when sign of y changes, we have \"straddled\" the solution, the root, the answer.<BR>\n" );
document.write( "we then look at a more precise value of x and repeat the process.\r<BR>\n" );
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document.write( "So, <BR>\n" );
document.write( "start with x=-1... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-1%29%5E3+%2B+2%28-1%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-1%29%5E3+%2B+2%28-1%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> -1 + 2 + 2 --> +ve<BR>\n" );
document.write( "now, try x = -2... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2%29%5E3+%2B+2%28-2%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-2%29%5E3+%2B+2%28-2%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> -8 + 8 + 2 --> +ve but getting closer to zero<BR>\n" );
document.write( "now try x = -3... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-3%29%5E3+%2B+2%28-3%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-3%29%5E3+%2B+2%28-3%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> -27 + 18 + 2 --> -ve\r<BR>\n" );
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document.write( "So the root lies between x=-2 and x=-3.\r<BR>\n" );
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document.write( "Now pick x=-2.5... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2.5%29%5E3+%2B+2%28-2.5%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-2.5%29%5E3+%2B+2%28-2.5%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> -ve, so the root lies between x=-2 and x=-2.5\r<BR>\n" );
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document.write( "So, pick x=-2.4... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2.4%29%5E3+%2B+2%28-2.4%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-2.4%29%5E3+%2B+2%28-2.4%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> -ve, Just. The root lies between x=-2 and x=-2.4\r<BR>\n" );
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document.write( "Pick x=-2.3... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-2.3%29%5E3+%2B+2%28-2.3%29%5E2+%2B+2 ALIGN=MIDDLE  ALT=\"y=%28-2.3%29%5E3+%2B+2%28-2.3%29%5E2+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> +ve, so the root lies now between x=-2.3 and x=-2.4.\r<BR>\n" );
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document.write( "So now you try say x=-2.35 and work out the bounds of the root etc.\r<BR>\n" );
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document.write( "Looking at the graph, we do indeed see a solution between -2 and -3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-10%2C10%2Cx%5E3%2B2x%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-10%2C10%2Cx%5E3%2B2x%5E2%2B2%29\"   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=graph%28300%2C300%2C-4%2C-2%2C-5%2C5%2Cx%5E3%2B2x%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-4%2C-2%2C-5%2C5%2Cx%5E3%2B2x%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a closer look at the root.\r<BR>\n" );
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document.write( "jon<BR>\n" );
document.write( " </SPAN>\n" );
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