document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442413>Question 442413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help.  I do not understand 2 problems and I have been working on them for hours now?? Thanks so much!<BR>\n" );
document.write( "1. Solve w^4-12w^2-2=0\r<BR>\n" );
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document.write( "2. Write the quadratic equation in the variable x having the given numbers as solutions.  Type the equation in standard form ax^2+bx+c=0.<BR>\n" );
document.write( "-(sqrt)2, 7 (sqrt)2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305144 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Let x = w^2<BR>\n" );
document.write( "Then we can write the equation as<BR>\n" );
document.write( "x^2 - 12x - 2 = 0<BR>\n" );
document.write( "Since the factorization is not obvious, solve using the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%2812%5E2+%2B+8%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%2812%5E2+%2B+8%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=x+=+%2812+%2B-+sqrt%28152%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28152%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "152 can be factored as 4*38, so we can simplify the radical:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+2sqrt%2838%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+2sqrt%2838%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6+%2B-+sqrt%2838%29 ALIGN=MIDDLE  ALT=\"x+=+6+%2B-+sqrt%2838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+w%5E2 ALIGN=MIDDLE  ALT=\"x+=+w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"w+=+sqrt%28x%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%286+%2B-+sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w+=+sqrt%286+%2B-+sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%286+%2B-+sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"-sqrt%286+%2B-+sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If we are restricting ourselves to real numbers, we can't take the square root<BR>\n" );
document.write( "of a negative number so the two solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+sqrt%286+%2B+sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"w+=+sqrt%286+%2B+sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%286+%2B+sqrt%2838%29%29 ALIGN=MIDDLE  ALT=\"-sqrt%286+%2B+sqrt%2838%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [approximately +-3.5]<BR>\n" );
document.write( "This is a bit messy, but as a check of our result we can graph the function and look for the zero crossings.<BR>\n" );
document.write( "We see that the function crosses the x-axis around x = -3.5 and x = 3.5.  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-40%2C40%2Cx%5E4-12x%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-40%2C40%2Cx%5E4-12x%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. If the two roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%282%29 ALIGN=MIDDLE  ALT=\"-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"7%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the equation can be factored as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bsqrt%282%29%29%28x-7sqrt%282%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2Bsqrt%282%29%29%28x-7sqrt%282%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply using FOIL and collect terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-6sqrt%282%29x+-+14+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-6sqrt%282%29x+-+14+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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