document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205913>Question 1205913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve x^4+64=20x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843005 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=843005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> subtract 20x^2 from both sides to get:<BR>\n" );
document.write( "x^4 + 64 - 20x^2 = 0<BR>\n" );
document.write( "arrange in descending order of degree to get:<BR>\n" );
document.write( "x^4 - 20x^2 + 64 = 0<BR>\n" );
document.write( "let y = x^2 to get:<BR>\n" );
document.write( "y^2 - 20y + 64 = 0<BR>\n" );
document.write( "factor to get:<BR>\n" );
document.write( "(y-4) * (y-16) = 0<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 4 or y = 16<BR>\n" );
document.write( "since y = x^2, you get:<BR>\n" );
document.write( "x = plus or minus 2 or x = plus or minus 4\r<BR>\n" );
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document.write( "your solutions are x = 2, -2, 4, -4\r<BR>\n" );
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document.write( "plug each of those into the original equation and the original equation will be true.\r<BR>\n" );
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document.write( "for example, when x = 4, x^4 + 64 = 80x^2 becomes 320 = 320, which is true and when x = 2, x^4 + 64 = 20x^2 becomes 80 = 80\r<BR>\n" );
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document.write( "here's what it looks like when you graph y = x^4 - 20x^2 + 64.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/020101.jpg\">\r<BR>\n" );
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document.write( "here's what it looks like when you graph y = x^2 + 64 and you graph y = 20x^2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/020102.jpg\">\r<BR>\n" );
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document.write( "the first graph shows the intersection of the graphed equation with y = 0.\r<BR>\n" );
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document.write( "the second graph shows the intersection of the two graphed equations.\r<BR>\n" );
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document.write( "the x-value of the intersection is the same in both graphs.\r<BR>\n" );
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