document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=765779>Question 765779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation in the real number system. 7x^3+3x^2-29x+11=0 <BR>\n" );
document.write( "What are the reals solutions of the equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #466416 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=466416\">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=7x%5E3%2B3x%5E2-29x%2B11=0+ ALIGN=MIDDLE  ALT=\"7x%5E3%2B3x%5E2-29x%2B11=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor, write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x%5E2-11x%5E2 ALIGN=MIDDLE  ALT=\"14x%5E2-11x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-29x ALIGN=MIDDLE  ALT=\"-29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x-22x ALIGN=MIDDLE  ALT=\"-7x-22x\"   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=7x%5E3%2B14x%5E2-7x-11x%5E2-22x%2B11=0+ ALIGN=MIDDLE  ALT=\"7x%5E3%2B14x%5E2-7x-11x%5E2-22x%2B11=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287x%5E3-11x%5E2%29%2B%2814x%5E2-22x%29-%287x-11%29=0+ ALIGN=MIDDLE  ALT=\"%287x%5E3-11x%5E2%29%2B%2814x%5E2-22x%29-%287x-11%29=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%287x-11%29%2B2x%287x-11%29-%287x-11%29=0+ ALIGN=MIDDLE  ALT=\"x%5E2%287x-11%29%2B2x%287x-11%29-%287x-11%29=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=%287x-11%29%28x%5E2%2B2x-1%29+=+0 ALIGN=MIDDLE  ALT=\"%287x-11%29%28x%5E2%2B2x-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x-11=+0 ALIGN=MIDDLE  ALT=\"7x-11=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=11 ALIGN=MIDDLE  ALT=\"7x=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F7 ALIGN=MIDDLE  ALT=\"x=11%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to find other two roots, use quadratic formula and solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-1+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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-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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%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=x+=+%28-2+%2B-+sqrt%28+4%2B4%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4%2B4%29%29%2F2+\"   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+8%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+8%29%29%2F2+\"   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-+2.83%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+2.83%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B2.83%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B2.83%29%2F2+\"   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+=+0.83%2F2+ ALIGN=MIDDLE  ALT=\"x+=+0.83%2F2+\"   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+=+0.415+ ALIGN=MIDDLE  ALT=\"x+=+0.415+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+-2.83%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+-2.83%29%2F2+\"   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+=-4.83%2F2+ ALIGN=MIDDLE  ALT=\"x+=-4.83%2F2+\"   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+=+-2.415+ ALIGN=MIDDLE  ALT=\"x+=+-2.415+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your solutions are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=11%2F7 ALIGN=MIDDLE  ALT=\"x=11%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0.415+ ALIGN=MIDDLE  ALT=\"x+=+0.415+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2.415+ ALIGN=MIDDLE  ALT=\"x+=+-2.415+\"   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%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+35%2C7x%5E3%2B3x%5E2-29x%2B11%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+5%2C+-10%2C+35%2C7x%5E3%2B3x%5E2-29x%2B11%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );