document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=807901>Question 807901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain why the equation (x-1)^2 +(x+1)^2 = 0 has no real roots.\r<BR>\n" );
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document.write( "Can you please help me out? Thanks so much in advance :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #486607 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=486607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-1)^2 +(x+1)^2 = 0\r<BR>\n" );
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document.write( "x^2 - 2x + 1 + x^2 + 2x + 1 = 0 ... FOIL/expand\r<BR>\n" );
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document.write( "2x^2 + 2 = 0 ... Combine like terms.\r<BR>\n" );
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document.write( "2x^2 = -2 ... Subtract 2 from both sides.\r<BR>\n" );
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document.write( "x^2 = -2/2 ... Divide both sides by 2.\r<BR>\n" );
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document.write( "x^2 = -1\r<BR>\n" );
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document.write( "So at this point, we can see that the equation won't have any real roots. Why? Because solving x^2 = -1 gives us x = i or x = -i, both of which are not real.\r<BR>\n" );
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document.write( "Note: <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;\" > which is an imaginary (not real) number </SPAN>\n" );
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