document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319350>Question 319350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Type an exact answer using radicals as needed and use commas to separate answers. What is the solution? w = \r<BR>\n" );
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document.write( "w^4 - 2w^2 - 2 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228715 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=228715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> w^4 - 2w^2 - 2 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find w^2 using the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in this equation<BR>\n" );
document.write( "x=w^2, a=1, b=-2, c=-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%28-%28-2%29+%2B-+sqrt%28-2%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%28-%28-2%29+%2B-+sqrt%28-2%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%282+%2B-+sqrt%284+-+%28-8%29+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+%2B-+sqrt%284+-+%28-8%29+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%282+%2B+sqrt%2812+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+%2B+sqrt%2812+%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=w%5E2+=+%282+%2B+sqrt%284%2A3%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+%2B+sqrt%284%2A3%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "extract the sqrt of 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%282+%2B+2%2Asqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+%2B+2%2Asqrt%283%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel the 2's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+1+%2B+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"w%5E2+=+1+%2B+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the square root of both sides<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; a good solution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "but we also have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%282+-+sqrt%2812+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+-+sqrt%2812+%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=w%5E2+=+%282+-+sqrt%284%2A3%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+-+sqrt%284%2A3%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "extract the sqrt of 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+%282+-+2%2Asqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"w%5E2+=+%282+-+2%2Asqrt%283%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel the 2's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2+=+1+-+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"w%5E2+=+1+-+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the square root of both sides<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%281-sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However sqrt of 3 > 1, therefore we have square root of a neg number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I'm going to say the exact solution using radicals<BR>\n" );
document.write( "w = +<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Confirm this with a graph of this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+4%2C+x%5E4-2x%5E2-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+4%2C+x%5E4-2x%5E2-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );