document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92081>Question 92081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this problem. this is the work i did so far: \r<BR>\n" );
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document.write( "there is a triangle on one side there is (x-2) the other side is (x-4) and the longest side is 10.\r<BR>\n" );
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document.write( "(x-2)^2+ (x-4)^2= 10^2<BR>\n" );
document.write( "(x-2)(x-2)+ (x-4)(x-4)= 100 <BR>\n" );
document.write( "x^2 + -2x + -2x + 4 + x^2 + -4x + -4x + 16 <BR>\n" );
document.write( "2x^2 + -12x + 20 = 100 \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 #66918 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=66918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll pick up where you left off (your steps are correct)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-12x+%2B+20+=+100+ ALIGN=MIDDLE  ALT=\"2x%5E2+-12x+%2B+20+=+100+\"   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+-12x+%2B+20+-+100=0+ ALIGN=MIDDLE  ALT=\"2x%5E2+-12x+%2B+20+-+100=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 100 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-12x+-80=0+ ALIGN=MIDDLE  ALT=\"2x%5E2+-12x+-80=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Now let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\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( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ax%5E2-12%2Ax-80=0 ALIGN=MIDDLE  ALT=\"2%2Ax%5E2-12%2Ax-80=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-12 ALIGN=MIDDLE  ALT=\"b=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-80 ALIGN=MIDDLE  ALT=\"c=-80\"   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--12+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A-80+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%28--12+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A-80+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=2, b=-12, and c=-80\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A-80+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A2%2A-80+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -12 to get 12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+144-4%2A2%2A-80+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+144-4%2A2%2A-80+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -12 to get 144  (note: remember when you square -12, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%5E2=-12%2A-12=144 ALIGN=MIDDLE  ALT=\"%28-12%29%5E2=-12%2A-12=144\"   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+=+%2812+%2B-+sqrt%28+144%2B640+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+144%2B640+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-80%2A2 ALIGN=MIDDLE  ALT=\"-4%2A-80%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=640 ALIGN=MIDDLE  ALT=\"640\"   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+=+%2812+%2B-+sqrt%28+784+%29%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+784+%29%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+28%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+28%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+28%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+28%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 2 to get 4\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B+28%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B+28%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+-+28%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%2812+-+28%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lets look at the first part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812+%2B+28%29%2F4 ALIGN=MIDDLE  ALT=\"x=%2812+%2B+28%29%2F4\"   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=40%2F4 ALIGN=MIDDLE  ALT=\"x=40%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So one answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets look at the second part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2812+-+28%29%2F4 ALIGN=MIDDLE  ALT=\"x=%2812+-+28%29%2F4\"   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=-16%2F4 ALIGN=MIDDLE  ALT=\"x=-16%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator\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;\" > Divide\r<BR>\n" );
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document.write( "So another answer is\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;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "Now lets find each of the leg's lengths:\r<BR>\n" );
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document.write( "Leg A: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-2=8 ALIGN=MIDDLE  ALT=\"10-2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2=-6 ALIGN=MIDDLE  ALT=\"-4-2=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=-4\r<BR>\n" );
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document.write( "Since a negative length doesn't make sense, the solution x=-4 must be discarded\r<BR>\n" );
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document.write( "Leg B: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-4=6 ALIGN=MIDDLE  ALT=\"10-4=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-4=-8 ALIGN=MIDDLE  ALT=\"-4-4=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in x=-4\r<BR>\n" );
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document.write( "Since a negative length doesn't make sense, the solution x=-4 must be discarded\r<BR>\n" );
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document.write( "So the only solution is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10 ALIGN=MIDDLE  ALT=\"x=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >  where the lengths of the legs are 8 and 6 (or 6 and 8) </SPAN>\n" );
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