document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7071>Question 7071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this problem forever and can not come up with the answer in the back of my book.\r<BR>\n" );
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document.write( "Please help me solve the following equation :  \r<BR>\n" );
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document.write( "&#9474;x^2 + 5&#9474; + &#9474;x - 2&#9474; &#8804; 8 \r<BR>\n" );
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document.write( "This is what I did .\r<BR>\n" );
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document.write( "&#9474;x^2 + 5 + x - 2&#9474;&#8804; 8\r<BR>\n" );
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document.write( "-8 &#8804; x^2 + 5 + x – 2 &#8804; 8\r<BR>\n" );
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document.write( "-8 &#8804; x^2 + x + 3 &#8804; 8<BR>\n" );
document.write( "then subtract -3 from all sides and get this\r<BR>\n" );
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document.write( "-11 &#8804; x^2 + x  &#8804; 5, Then completing square for middle getting this\r<BR>\n" );
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document.write( "-11 + 1/4 &#8804; x^2 + x + 1/4 &#8804; 5 + 1/4\r<BR>\n" );
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document.write( "-43/4 &#8804; x^2 + x + 1/4 &#8804; 21/4\r<BR>\n" );
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document.write( "-43/4 &#8804; (x + 1/2)^2 &#8804; 21/4\r<BR>\n" );
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document.write( "Then don’t go any further because I now that I can not get the answer that is in the book.\r<BR>\n" );
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document.write( "Please tell me where I am going wrong.\r<BR>\n" );
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document.write( "TIA,<BR>\n" );
document.write( "del<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 #3888 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=3888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  &#9474;x^2 + 5&#9474; + &#9474;x - 2&#9474; &#8804; 8  ...(**)<BR>\n" );
document.write( " You did wrong at very first step,because you did not apply the def. of abs<BR>\n" );
document.write( " value correctly.\r<BR>\n" );
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document.write( " Note that x^2 + 5 is always positive, so  |x^2 + 5| = x^2 + 5.\r<BR>\n" );
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document.write( " Case (i) if x - 2 >= 0, then |x-2| = x-2 ,so (**) converts to<BR>\n" );
document.write( "  x^2 + 5  + x - 2 &#8804; 8  <BR>\n" );
document.write( " [Also, don't write garbages like adding -8 on both sides]<BR>\n" );
document.write( " or x^2 + x -5 <= 0.<BR>\n" );
document.write( "  Since [-1 +/- sqrt(21)]/2 are the two roots of x^2 + x -5 = 0  <BR>\n" );
document.write( "  x^2 + x -5 <= 0 implies  [-1 - sqrt(21)]/2 <= x <= (-1 + sqrt(21))/2<BR>\n" );
document.write( "  (between these two roots).\r<BR>\n" );
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document.write( "  But x >=2, and (-1 + sqrt(21))/2 < (1 + sqt(25)/2  = 2, a contradiction. <BR>\n" );
document.write( "  This means there is nosulution in this case.\r<BR>\n" );
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document.write( " Case (i) if x - 2 < 0, then |x-2| = -x+2 ,so (**) converts to<BR>\n" );
document.write( "  x^2 + 5  - x + 2 &#8804; 8 or<BR>\n" );
document.write( "  x^2 - x  -1 <= 0.<BR>\n" );
document.write( "  <BR>\n" );
document.write( " two roots of x^2 - x -1 = 0 are  [1 +/- sqrt(5)]/2  <BR>\n" );
document.write( " Hence,   (-1 - sqrt(5))/2 <= x <= (-1 + sqrt(5))/2<BR>\n" );
document.write( " Since x -2 < 0, so x < 2 and we see that (-1 + sqrt(5))/2 <2 [OK}<BR>\n" );
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document.write( " The solution set is [(-1 - sqrt(5))/2,(-1 - sqrt(5))/2 ]<BR>\n" );
document.write( " or (-1 - sqrt(5))/2 <= x <= (-1 + sqrt(5))/2\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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