document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553819>Question 553819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2B4x%5E3%2B2x%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E4%2B4x%5E3%2B2x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real numbers.<BR>\n" );
document.write( "This is what i have so far.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x%5E2%2B4x%2B2%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%28x%5E2%2B4x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then I can set x^2=0 and get x=0 after taking the square root of both sides.\r<BR>\n" );
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document.write( "then the problem that is left is a quadratic so i can use the quadratic formula and get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B+or+-sqrt%284%5E2-4%2A1%2A2%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x=%28-4%2B+or+-sqrt%284%5E2-4%2A1%2A2%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "after i combine every thing i get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4%2B+or+-+sqrt%288%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-4%2B+or+-+sqrt%288%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the answer in the back of the book is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Bor+-+sqrt%282%29 ALIGN=MIDDLE  ALT=\"-2%2Bor+-+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i see how -4 is smiplified down to -2 what i don't understand is how you get the sqrt2 out of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%288%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Am i completly off track or did i miss something. please help if you can<BR>\n" );
document.write( "thanks Kathleen Nolan </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #361085 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=361085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are close!!  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2B-sqrt%288%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-4%2B-sqrt%288%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2B-sqrt%284%29%2Asqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-4%2B-sqrt%284%29%2Asqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2B-2%2Asqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-4%2B-2%2Asqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor the 2 in the numerator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%28-2%2B-sqrt%282%29%29%29%2F2 ALIGN=MIDDLE  ALT=\"+%282%28-2%2B-sqrt%282%29%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide out the 2, and you will have the correct answer!!<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B-sqrt%282%29+ ALIGN=MIDDLE  ALT=\"-2%2B-sqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You may want to see my FREE website for additional explanation on this topic.  The easiest way to find the website is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com.  Near the bottom of this page is a link that takes you to my Homepage.  On my Homepage, look for the link \"Basic, Intermediate, and College Algebra: One Step at a Time.\"  Choose \"Basic Algebra\" and look in Chapter 5 for the section on Reducing Fractions with Radicals.  There is also an explanation in \"Intermediate Algebra\", \"Chapter 3.\"  I think you will really like the \"Math in Living Color\" pages that go with these sections.  \r<BR>\n" );
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document.write( "If you need to contact me, send me an Email at rapaljer@seminolestate.edu.\r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus </SPAN>\n" );
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