document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128015>Question 128015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having such a time understanding how to solve...<BR>\n" );
document.write( "w^4 - 20w^2 - 2 = 0.<BR>\n" );
document.write( "It is not qudratic but is to be reduced to a quadratic equation in order for us to solve it. It is said to be reducible to quadratic.\r<BR>\n" );
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document.write( "I know we have to substitute u for w^2. So then the equation would be <BR>\n" );
document.write( "u^2 - 20u - 2 = 0\r<BR>\n" );
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document.write( "Solving for u is...<BR>\n" );
document.write( "u = 10 - radical sign 102 and<BR>\n" );
document.write( "u = 10 + radical sign 102\r<BR>\n" );
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document.write( "I know the solutions are:<BR>\n" );
document.write( "10 - radical sign 102 all under the same radical sign , <BR>\n" );
document.write( "10 + radical sign under radical sign 102 all under the same radical sign ,<BR>\n" );
document.write( "10 - radical sign under radical sign 102 all under the same negative radical sign ,<BR>\n" );
document.write( "10 + radical sign under radical sign 102 all under the same negative radical sign \r<BR>\n" );
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document.write( "My question is: Where did they get 10 and 102? I guess I do not know how to solve for u. <BR>\n" );
document.write( "Can You please show the steps for this problem?<BR>\n" );
document.write( "This does not come from a book.<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 #93736 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93736\">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=u%5E2+-+20u+-+2+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+-+20u+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the general solution to the quadratic equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=au%5E2%2Bbu%2Bc=0 ALIGN=MIDDLE  ALT=\"au%5E2%2Bbu%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "For your equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=red%281%29 ALIGN=MIDDLE  ALT=\"a=red%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=green%28-20%29 ALIGN=MIDDLE  ALT=\"b=green%28-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=blue%28-2%29 ALIGN=MIDDLE  ALT=\"c=blue%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%28-%28green%28-20%29%29+%2B-+sqrt%28%28green%28-20%29%29%5E2-4%2Ared%281%29%2A%28blue%28-2%29%29+%29%29%2F%282%2Ared%281%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%2820+%2B-+sqrt%28400%2B8%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"u+=+%2820+%2B-+sqrt%28400%2B8%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+%2820+%2B-+sqrt%28408%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"u+=+%2820+%2B-+sqrt%28408%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=408=4%2A102 ALIGN=MIDDLE  ALT=\"408=4%2A102\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28408%29=sqrt%284%29%2Asqrt%28102%29=2%2Asqrt%28102%29 ALIGN=MIDDLE  ALT=\"sqrt%28408%29=sqrt%284%29%2Asqrt%28102%29=2%2Asqrt%28102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+10+%2B+sqrt%28102%29 ALIGN=MIDDLE  ALT=\"u+=+10+%2B+sqrt%28102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+10+-+sqrt%28102%29 ALIGN=MIDDLE  ALT=\"u+=+10+-+sqrt%28102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But remember, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=w%5E2 ALIGN=MIDDLE  ALT=\"u=w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=+%2B+sqrt%28u%29 ALIGN=MIDDLE  ALT=\"w=+%2B+sqrt%28u%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+-sqrt%28u%29 ALIGN=MIDDLE  ALT=\"w+=+-sqrt%28u%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=w=%2Bsqrt%2810+%2B+sqrt%28102%29%29 ALIGN=MIDDLE  ALT=\"w=%2Bsqrt%2810+%2B+sqrt%28102%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%2Bsqrt%2810+-+sqrt%28102%29%29 ALIGN=MIDDLE  ALT=\"w=%2Bsqrt%2810+-+sqrt%28102%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%2810+%2B+sqrt%28102%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%2810+%2B+sqrt%28102%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%2810+-+sqrt%28102%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%2810+-+sqrt%28102%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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