document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=156836>Question 156836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to resolve x, AB, BC and AC, where A, B and C are points on a line.  A is leftmost, C is rightmost, and B is somewhere in between.\r<BR>\n" );
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document.write( "AB = 2x+1<BR>\n" );
document.write( "BC = x-2<BR>\n" );
document.write( "AC = sqrt (x^2 + 25x + 5)\r<BR>\n" );
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document.write( "Was able to write, 2x+1+x-2 = sqrt (x^2+25x+5), which reduces to 3x-1 = sqrt (x^2 + 25x + 5).\r<BR>\n" );
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document.write( "I don't know how to eliminate the square root, especially when there is an exponential along with it.\r<BR>\n" );
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document.write( "Please help.\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115629 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=115629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll start where you left off\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-1+=+sqrt+%28x%5E2+%2B+25x+%2B+5%29 ALIGN=MIDDLE  ALT=\"3x-1+=+sqrt+%28x%5E2+%2B+25x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-1%29%5E2+=+x%5E2+%2B+25x+%2B+5 ALIGN=MIDDLE  ALT=\"%283x-1%29%5E2+=+x%5E2+%2B+25x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides. This will eliminate the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-6x%2B1+=+x%5E2+%2B+25x+%2B+5 ALIGN=MIDDLE  ALT=\"9x%5E2-6x%2B1+=+x%5E2+%2B+25x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-6x%2B1-x%5E2-25x-5=0 ALIGN=MIDDLE  ALT=\"9x%5E2-6x%2B1-x%5E2-25x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x ALIGN=MIDDLE  ALT=\"25x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2-31x-4=0 ALIGN=MIDDLE  ALT=\"8x%5E2-31x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-31 ALIGN=MIDDLE  ALT=\"b=-31\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2-4%288%29%28-4%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2-4%288%29%28-4%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-31 ALIGN=MIDDLE  ALT=\"b=-31\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+%28-31%29%5E2-4%288%29%28-4%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+%28-31%29%5E2-4%288%29%28-4%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-31 ALIGN=MIDDLE  ALT=\"-31\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31 ALIGN=MIDDLE  ALT=\"31\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+961-4%288%29%28-4%29+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+961-4%288%29%28-4%29+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-31 ALIGN=MIDDLE  ALT=\"-31\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=961 ALIGN=MIDDLE  ALT=\"961\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+961--128+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+961--128+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%288%29%28-4%29 ALIGN=MIDDLE  ALT=\"4%288%29%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-128 ALIGN=MIDDLE  ALT=\"-128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+961%2B128+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+961%2B128+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28961--128%29 ALIGN=MIDDLE  ALT=\"sqrt%28961--128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28961%2B128%29 ALIGN=MIDDLE  ALT=\"sqrt%28961%2B128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+1089+%29%29%2F%282%288%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+1089+%29%29%2F%282%288%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=961 ALIGN=MIDDLE  ALT=\"961\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128 ALIGN=MIDDLE  ALT=\"128\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1089 ALIGN=MIDDLE  ALT=\"1089\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+sqrt%28+1089+%29%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+sqrt%28+1089+%29%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B-+33%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B-+33%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1089 ALIGN=MIDDLE  ALT=\"1089\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33 ALIGN=MIDDLE  ALT=\"33\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+%2B+33%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+%2B+33%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831+-+33%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=+%2831+-+33%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2864%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=+%2864%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-2%29%2F%2816%29 ALIGN=MIDDLE  ALT=\"x+=++%28-2%29%2F%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F8 ALIGN=MIDDLE  ALT=\"x+=+-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F8 ALIGN=MIDDLE  ALT=\"x+=+-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F8 ALIGN=MIDDLE  ALT=\"x+=+-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > back into the original equation, you'll find that the equation won't be true. Also, since distance is <b>ALWAYS</b> positive, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F8 ALIGN=MIDDLE  ALT=\"x+=+-1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > will not work (since if you plug it into any expression the result is negative)\r<BR>\n" );
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document.write( "So the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into AB,BC, and AC:\r<BR>\n" );
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document.write( "AB = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1=2%284%29%2B1=8%2B1=9 ALIGN=MIDDLE  ALT=\"2x%2B1=2%284%29%2B1=8%2B1=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "BC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=%284%29-2=2 ALIGN=MIDDLE  ALT=\"x-2=%284%29-2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "AC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28x%5E2+%2B+25x+%2B+5%29+=sqrt+%28%284%29%5E2+%2B+25%284%29+%2B+5%29=sqrt+%2816+%2B+100+%2B+5%29=sqrt+%28121%29=11 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the three lengths are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=9 ALIGN=MIDDLE  ALT=\"AB=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=2 ALIGN=MIDDLE  ALT=\"BC=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=11 ALIGN=MIDDLE  ALT=\"AC=11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Remember, the segment addition postulate is AB+BC=AC (ie the lengths of the pieces of AC should add to the length of AC)\r<BR>\n" );
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document.write( "AB+BC=AC ... Start with the given equation\r<BR>\n" );
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document.write( "9+2=11 ...Plug in AB=9, BC=2, and AC=11\r<BR>\n" );
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document.write( "11=11 ... Add. Since this equation is true, this verifies the answer. </SPAN>\n" );
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