document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972200>Question 972200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Absolute value of (x^2 +6)= 5x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594608 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> split this up into two pieces.\r<BR>\n" );
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document.write( "if the expression within the absolute value sign is positive, then you get:\r<BR>\n" );
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document.write( "x^2 + 6 = 5x\r<BR>\n" );
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document.write( "subtract 5x from both sides of that equation and you get:<BR>\n" );
document.write( "x^2 - 5x + 6 = 0<BR>\n" );
document.write( "factor that quadratic equation to get:<BR>\n" );
document.write( "(x-3)(x-2) = 0<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "x = 2\r<BR>\n" );
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document.write( "if the expression within the absolute value sign is negative, then you get:\r<BR>\n" );
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document.write( "x^2 + 6 = -5x<BR>\n" );
document.write( "add 5x to both sides of that equation to get:<BR>\n" );
document.write( "x^2 + 5x + 6 = 0<BR>\n" );
document.write( "factor that quadratic equation to get:<BR>\n" );
document.write( "(x+3)*(x+2) = 0<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "x = -2\r<BR>\n" );
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document.write( "your possible solutions are:\r<BR>\n" );
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document.write( "x = 2<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( "x = -3\r<BR>\n" );
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document.write( "x cannot be equal to -2 or -3 because than the absolute value is negative which is impossible because the absolute value of an expression is always positive.\r<BR>\n" );
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document.write( "so x has to be 2 or 3 or nothing at all.\r<BR>\n" );
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document.write( "replace x with 2 and replace x with 3 and you will see that the original equation is true.\r<BR>\n" );
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document.write( "abs(x^2+6) = abs(15) when x = 3 and 5x = 15 when x = 3<BR>\n" );
document.write( "abs(x^2+6) = abs(10) when x = 2 and 5x = 10 when x = 2\r<BR>\n" );
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document.write( "original equations confirm that the solution is correct.\r<BR>\n" );
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document.write( "here's a graph of the two equations.\r<BR>\n" );
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document.write( "you can see that they intersect when x = 2 and when x = 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/052602.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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