document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490208>Question 490208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> K is between J and L  JK=2x^2+3   KL=7x+4   JL=2x+10  Find JK\r<BR>\n" );
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document.write( "I have solved to 2x^2+5X=3, but that makes no sense and am lost.  Thanks for any help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333951 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=333951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> K is between J and L<BR>\n" );
document.write( "this means that JK + KL = JL\r<BR>\n" );
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document.write( "JK is equal to 2x^2 + 3<BR>\n" );
document.write( "KL is equal to 7x+4<BR>\n" );
document.write( "JL is equal to 2x+10\r<BR>\n" );
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document.write( "since JK + KL = JL, this means that:<BR>\n" );
document.write( "2x^2 + 3 + 7x+4 = 2x+10\r<BR>\n" );
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document.write( "you want to solve for x.<BR>\n" );
document.write( "once you solve for x, then you can solve for the value of JK.\r<BR>\n" );
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document.write( "your equation to work with is:<BR>\n" );
document.write( "2x^2 + 3 + 7x + 4 = 2x + 10<BR>\n" );
document.write( "subtract 2x from both sides of the equation and subtract 10 from both sides of the equation to get:<BR>\n" );
document.write( "2x^2 + 3 + 7x + 4 - 2x - 10 = 0<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "2x^2 + 5x - 3 = 0<BR>\n" );
document.write( "this is a quadratic equation that can be solved for the value of x.<BR>\n" );
document.write( "the factors to this equation are:<BR>\n" );
document.write( "(2x - 1) * (x + 3) = 0<BR>\n" );
document.write( "this equation is true if (2x - 1) = 0 or (x + 3) = 0 or both are equal to 0.<BR>\n" );
document.write( "solving for 2x - 1 = 0 gets x = 1/2<BR>\n" );
document.write( "solving for x + 3 = 0 gets x = -3\r<BR>\n" );
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document.write( "since we are talking about the length of JK, KL, AND JL, then the length must be positive so the only answer that is acceptable is x = 1/2\r<BR>\n" );
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document.write( "when x = 1/2, we get:\r<BR>\n" );
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document.write( "JK = 2x^2 + 3 which results in JK = 3.5<BR>\n" );
document.write( "KL = 7x + 4 which results in KL = 7.5<BR>\n" );
document.write( "JL = 2x + 10 which results in JL = 11\r<BR>\n" );
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document.write( "since JK + KL = JL, then we should get 11 = 11<BR>\n" );
document.write( "JK + KL = 3.5 + 7.5 = 11<BR>\n" );
document.write( "we're good.\r<BR>\n" );
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document.write( "the value of x is confirmed as good which results in JK = 3.5 which answers the question.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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