document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101465>Question 1101465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find all real solutions to this equation:\r<BR>\n" );
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document.write( "4x^-4 -16x^-2+4 = 0\r<BR>\n" );
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document.write( "This is how a proceeded:\r<BR>\n" );
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document.write( "1/4x^4 - 1/16x^2 +4 = 0;     I figured x cannot equal zero, and the LCD = 16x^4\r<BR>\n" );
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document.write( "I multiplied both sides by the LCD to clear the denominators:<BR>\n" );
document.write( "4 - x^2 + 64x^4 = 0<BR>\n" );
document.write( "or <BR>\n" );
document.write( "64x^4 -x^2 +4 = 0<BR>\n" );
document.write( "I made x^2 = w to get a quadratic equation:<BR>\n" );
document.write( "64w^2 -w +4 = 0\r<BR>\n" );
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document.write( "I tried factoring this, and I couldn't.  Then I figured out that the discriminant is less than zero, which will give me imaginary numbers   (b^2 -4ac = 1 -1024 = -1023)\r<BR>\n" );
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document.write( "This can't possibly be right, so I must be doing something wrong.  Can you help?  <BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716044 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=716044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  find all real solutions to this equation: <BR>\n" );
document.write( "4x^-4 -16x^-2+4 = 0 <BR>\n" );
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document.write( "Let w = x^-2<BR>\n" );
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document.write( "Substitute to get:<BR>\n" );
document.write( "4w^2 - 16w + 4 = 0<BR>\n" );
document.write( "---------------(----------<BR>\n" );
document.write( "Solve for \"w\"::<BR>\n" );
document.write( "4(w^2 - 4w + 1) = 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Quadratic Formula::<BR>\n" );
document.write( "w = [4 +- sqrt(16-4*1*1)]/2<BR>\n" );
document.write( "w = [4 +- sqrt(12)]/2<BR>\n" );
document.write( "w = 2 +- 2sqrt(3)<BR>\n" );
document.write( "w = -1.4641 or w = 5.4641<BR>\n" );
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document.write( "Ans:: x = 0.1830.. or x = -0.6830..<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( " </SPAN>\n" );
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