document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165009>Question 165009</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.		\r<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 #121621 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Draw a picture of the problem -- label everything you know -- this helps!<BR>\n" );
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document.write( "Let x = length of the ladder<BR>\n" );
document.write( "x-3 = distance  from the bottom of the ladder to the wall<BR>\n" );
document.write( "x-4 = distance of its top to the ground<BR>\n" );
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document.write( "Since the wall the the ground forms a right angle, this is a \"right triangle\".  We can apply Pythagorean theorem:<BR>\n" );
document.write( "(x-3)^2 + (x-4)^2 = x^2<BR>\n" );
document.write( "x^2-6x+9 + x^2-8x+16 = x^2<BR>\n" );
document.write( "2x^2-14x+25 = x^2<BR>\n" );
document.write( "x^2-14x+25 = 0<BR>\n" );
document.write( "Since we can't factor, we must resort to the quadratic formula.  Doing so, will result in:<BR>\n" );
document.write( "x = {11.90, 2.10}<BR>\n" );
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document.write( "We can toss out the 2.10 answer leaving us with:<BR>\n" );
document.write( "11.90 feet (length of the ladder)<BR>\n" );
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document.write( "Details of quadratic:<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-14x%2B25+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-14x%2B25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-14%29%5E2-4%2A1%2A25=96 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-14%29%5E2-4%2A1%2A25=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=96 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--14%2B-sqrt%28+96+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--14%2B-sqrt%28+96+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+11.8989794855664 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+11.8989794855664\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-14%29-sqrt%28+96+%29%29%2F2%5C1+=+2.10102051443364 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-14%29-sqrt%28+96+%29%29%2F2%5C1+=+2.10102051443364\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-14x%2B25 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-14x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-14x%2B25+=+1%28x-11.8989794855664%29%2A%28x-2.10102051443364%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-14x%2B25+=+1%28x-11.8989794855664%29%2A%28x-2.10102051443364%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 11.8989794855664, 2.10102051443364.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-14%2Ax%2B25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-14%2Ax%2B25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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