document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=709876>Question 709876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve x^3+x=0 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #436803 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=436803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve for x, first factor an x from the left side of the equal sign, since x is common to both terms.  This gives us\r<BR>\n" );
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document.write( "x(x^2 + 1) = 0\r<BR>\n" );
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document.write( "We know that x = 0, because if you multiply any number by 0, you get zero, so if you substitute 0 into the factored equation\r<BR>\n" );
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document.write( "0(0^2 + 1)\r<BR>\n" );
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document.write( "We get 0.\r<BR>\n" );
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document.write( "Now, to find the other values of x,  set (x^2 + 1) equal to 0:  x^2 + 1 = 0\r<BR>\n" );
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document.write( "To solve for x, subtract 1 from both sides of the equation, which gives us\r<BR>\n" );
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document.write( "x^2 = -1\r<BR>\n" );
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document.write( "Since we are squaring the x, we must take the square root of both sides, to remove the exponent of 2.  This gives us\r<BR>\n" );
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document.write( "Our final two answers for x will be imaginary numbers.  Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, i will be the second value of x.  Remember, when you take the square root of a square, your result is both a positive AND negative number.  Therefore, your third and final value of x, is -i\r<BR>\n" );
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document.write( "Answer:  x = 0, i, -i </SPAN>\n" );
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