document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830950>Question 830950</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate x from  x^3+3=x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #520737 by </B><A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><B>tommyt3rd(5050)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tommyt3rd><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=tommyt3rd><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=520737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll use numerical methods.\r<BR>\n" );
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document.write( "Graphing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B3 ALIGN=MIDDLE  ALT=\"x%5E3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > together shows that there is only one point of intersection - slightly less than -1. So we know that there is only 1 real solution.\r<BR>\n" );
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document.write( "We use Newton's method:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-x%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-x%5E2%2B3\"   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=df%2Fdx=3x%5E2-2x ALIGN=MIDDLE  ALT=\"df%2Fdx=3x%5E2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bn%2B1%5D=x%5Bn%5D-%28x%5Bn%5D%5E3-x%5Bn%5D%5E2%2B3%29%2F%283x%5Bn%5D%5E2-2x%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"x%5Bn%2B1%5D=x%5Bn%5D-%28x%5Bn%5D%5E3-x%5Bn%5D%5E2%2B3%29%2F%283x%5Bn%5D%5E2-2x%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We wont bother simplifying because we'll do the calculations by calculator:\r<BR>\n" );
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document.write( "guess x=-1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-6%2F5 ALIGN=MIDDLE  ALT=\"x%5B2%5D=-6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=-47%2F40 ALIGN=MIDDLE  ALT=\"x%5B3%5D=-47%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=-1.1745595 ALIGN=MIDDLE  ALT=\"x%5B4%5D=-1.1745595\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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