document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=370127>Question 370127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been stuck on this problem for a really long time. I'm trying to figure out a problem reducible to a quadratic equation in a step by step method so I can understand how I get from one point to the other. \r<BR>\n" );
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document.write( "The problem is: w^4-6w^2-2=0<BR>\n" );
document.write( "I only know this:\r<BR>\n" );
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document.write( "u = w^2\r<BR>\n" );
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document.write( "From my text and all the research I've done, I also know that I would rewrite this problem as:\r<BR>\n" );
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document.write( "u^2 - 6u - 2 = 0\r<BR>\n" );
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document.write( "I have to solve this but it's not factorable which is where I am absolutely stumped. This is an example problem on my homework I'm providing here so I have the answers for that but I just don't know how they got them.\r<BR>\n" );
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document.write( "This is the way they worked it out.....\r<BR>\n" );
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document.write( "u^2-6u-2=0<BR>\n" );
document.write( "they solve for u...but how????\r<BR>\n" );
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document.write( "they got the answer <BR>\n" );
document.write( "u=3-sqrt11 or u=3+sqrt11\r<BR>\n" );
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document.write( "then after this the problem needs to be solved for w.\r<BR>\n" );
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document.write( "Is there any way you can help and show me in a step by step fashion so I get this? Thank you. LeAnn<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #263779 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=263779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You found that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=3-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"u=3-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=3%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"u=3%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is completely correct. However, we want to solve for 'w'.\r<BR>\n" );
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document.write( "Recall that you let <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;\" >. \r<BR>\n" );
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document.write( "So plug this into the two equations above to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2=3-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"w%5E2=3-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2=3%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"w%5E2=3%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we need to solve each equation for 'w'. We'll do this by taking the square root of both sides.\r<BR>\n" );
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document.write( "So solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2=3-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"w%5E2=3-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for w to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%283-sqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%283-sqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%283-sqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%283-sqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2=3%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"w%5E2=3%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for w to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%283%2Bsqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%283%2Bsqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%283%2Bsqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%283%2Bsqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the four solutions are \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%283-sqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%283-sqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%283-sqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%283-sqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=sqrt%283%2Bsqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=sqrt%283%2Bsqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-sqrt%283%2Bsqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"w=-sqrt%283%2Bsqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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