document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171507>Question 171507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the triange with a hypotenuse = 20 , and one leg = X + 8 , and the other leg = X<BR>\n" );
document.write( "Approximate to the nearest foot how many feet of walking distance a person saves by cutting across the lawn instead of walking on the side walk.\r<BR>\n" );
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document.write( "I know you use pythagorean theorem to get {2x^2 + 16x -336 = 0}<BR>\n" );
document.write( "then simplify and get 2(x^2 + 8x - 168) = 0<BR>\n" );
document.write( "After this you use quadratic equation and get -4 +- ^736 over 1<BR>\n" );
document.write( "I dont know how to get the whole number after this<BR>\n" );
document.write( "Thanks \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 #126670 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You were headed down the right path but made one little mis-step.\r<BR>\n" );
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document.write( "Your equation is correct:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x-169=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x-169=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Your evaluation of the quadratic formula was correct up to a point, so let's review:\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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A1%2A%28-168%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A1%2A%28-168%29+%29%29%2F%282%2A1%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+=+%28-8+%2B-+sqrt%28+736+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-8+%2B-+sqrt%28+736+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  So far, so good.\r<BR>\n" );
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document.write( "But then you simplified to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4+%2B-+sqrt%28+736+%29+ ALIGN=MIDDLE  ALT=\"x+=+-4+%2B-+sqrt%28+736+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is incorrect because you only divided ONE of the numerator terms by the denominator.  That is against the rules:  the other team gets a penalty kick.\r<BR>\n" );
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document.write( "What you need to do is find the prime factorization of 736.\r<BR>\n" );
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document.write( "736/2 = 368<BR>\n" );
document.write( "368/2 = 184<BR>\n" );
document.write( "184/2 = 92<BR>\n" );
document.write( "92/2 = 46<BR>\n" );
document.write( "46/2 = 23<BR>\n" );
document.write( "23 is prime\r<BR>\n" );
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document.write( "Now you can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=736=23+%2A+2+%2A+2%5E4 ALIGN=MIDDLE  ALT=\"736=23+%2A+2+%2A+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28736%29=sqrt%2823+%2A+2+%2A+2%5E4%29=4%2Asqrt%2846%29 ALIGN=MIDDLE  ALT=\"sqrt%28736%29=sqrt%2823+%2A+2+%2A+2%5E4%29=4%2Asqrt%2846%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Going back to where you were before you went astray:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-8+%2B-+sqrt%28+736+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-8+%2B-+sqrt%28+736+%29%29%2F2+\"   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+=+%28-8+%2B-+4%2Asqrt%28+46+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-8+%2B-+4%2Asqrt%28+46+%29%29%2F2+\"   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+=+-4+%2B-+2%2Asqrt%28+46+%29+ ALIGN=MIDDLE  ALT=\"x+=+-4+%2B-+2%2Asqrt%28+46+%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=+-4+-+2%2Asqrt%28+46+%29+ ALIGN=MIDDLE  ALT=\"+-4+-+2%2Asqrt%28+46+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative, so exclude this root as extraneous.\r<BR>\n" );
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document.write( "  Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%2B+2%2Asqrt%28+46+%29+ ALIGN=MIDDLE  ALT=\"-4+%2B+2%2Asqrt%28+46+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which gets you approximately 9.56, the length of the short leg of the triangle.  Since the longer leg is 8 feet longer, the longer leg must be approximately 17.56 feet.  If you walk the sidewalk, you have to go 17.56 feet plus 9.56 feet or 27.12 feet.  If you walk the diagonal, you only have to walk 20 feet.  The difference is 27.12 - 20 = 7.12.  Rounded to the nearest foot, 7 feet.\r<BR>\n" );
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document.write( "Notice that I didn't do the round-off until the very last step.  Whenever you round numbers, you introduce errors, so it is important to keep greater precision (typically 1 or 2 decimal places greater precision than the precision required in the answer) until you have made your final calculation. </SPAN>\n" );
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