document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216520>Question 216520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a 13-foot ladder is leaning against a house. the distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. how far is the bottom of the ladder from the house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163484 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=163484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A 13-foot ladder is leaning against a house. The distance from the bottom of the ladder to the house is 7 feet less than the distance from the top of the ladder to the ground. How far is the bottom of the ladder from the house?\r<BR>\n" );
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document.write( "Step 1.  Let c=13 as hypotenuse.\r<BR>\n" );
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document.write( "Step 2.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the distance from the top of the ladder to the ground\r<BR>\n" );
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document.write( "Step 3.  Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-7 ALIGN=MIDDLE  ALT=\"y=x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the distance from the bottom of the ladder to the house\r<BR>\n" );
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document.write( "Step 4.  Use the Pythagorean Theorem which says that the sum of the squares of the legs (x and by)of a right triangle is equal to the sum of the hypotenuse c or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  Then substitute y of Step 3 into Step 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-7%29%5E2%2Bx%5E2=c%5E2=13%5E2 ALIGN=MIDDLE  ALT=\"%28x-7%29%5E2%2Bx%5E2=c%5E2=13%5E2\"   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=2x%5E2-14x%2B49=169 ALIGN=MIDDLE  ALT=\"2x%5E2-14x%2B49=169\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtracting 160 from both sides to get a quadratic equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-14x%2B49-169=169-169 ALIGN=MIDDLE  ALT=\"2x%5E2-14x%2B49-169=169-169\"   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=2x%5E2-14x-120=0 ALIGN=MIDDLE  ALT=\"2x%5E2-14x-120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5.  The quadratic formula will be used to sole the equation. The formula is given as\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%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where a=2, b=-14, and c=-120.\r<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=2x%5E2%2B-14x%2B-120+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-14x%2B-120+=+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" );
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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%2A2%2A-120=1156 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-14%29%5E2-4%2A2%2A-120=1156\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=1156 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+1156+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--14%2B-sqrt%28+1156+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+1156+%29%29%2F2%5C2+=+12 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+1156+%29%29%2F2%5C2+=+12\"   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+1156+%29%29%2F2%5C2+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-14%29-sqrt%28+1156+%29%29%2F2%5C2+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-14x%2B-120 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-14x%2B-120\"   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=2x%5E2%2B-14x%2B-120+=+2%28x-12%29%2A%28x--5%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-14x%2B-120+=+2%28x-12%29%2A%28x--5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -5.\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+2%2Ax%5E2%2B-14%2Ax%2B-120+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-14%2Ax%2B-120+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Pick the solution, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > , since we want positive lengths.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-7=20-7=5 ALIGN=MIDDLE  ALT=\"y=x-7=20-7=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 6.  ANSWER:  The distance from the bottom of the ladder to the house is 5 feet.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit \r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
document.write( " </SPAN>\n" );
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