document.write( "Question 585153: Use Phythagorean theorem to find x. The diagram is a right angle triange with leg a =x+3, leg b=x+10 and Hypotenuse =x+11.
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Algebra.Com's Answer #373172 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "                         a² + b² = c²\r\n" );
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document.write( "  So substitute (x + 3) for a, (x + 10) for b, and (x + 11) for c\r\n" );
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document.write( "            (x + 3)² + (x + 10)² = (x + 11)²\r\n" );
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document.write( "(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9 = (x² + 6x + 9)\r\n" );
document.write( "So substitute (x² + 6x + 9) for (x + 3)²\r\n" );
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document.write( "                   (x² + 6x + 9) + (x + 10)² = (x + 11)²\r\n" );
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document.write( "(x + 10)² = (x + 10)(x + 10) = x² + 10x + 10x + 100 = (x² + 20x + 100)\r\n" );
document.write( "So substitute (x² + 20x + 100) for (x + 10)²\r\n" );
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document.write( "                  (x² + 6x + 9) + (x² + 20x + 100)² = (x + 11)²\r\n" );
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document.write( "(x + 11)² = (x + 11)(x + 11) = x² + 11x + 11x + 121 = (x² + 22x + 121)\r\n" );
document.write( "So substitute (x² + 22x + 121) for (x + 11)²\r\n" );
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document.write( "                   (x² + 6x + 9) + (x² + 20x + 100) = (x² + 22x + 121)\r\n" );
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document.write( "                       x² + 6x + 9 + x² + 20x + 100 = x² + 22x + 121\r\n" );
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document.write( "                                    2x² + 26x + 109 = x² + 22x + 121\r\n" );
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document.write( "                                       x² + 4x - 12 = 0\r\n" );
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document.write( "                                     (x + 6)(x - 2) = 0\r\n" );
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document.write( "                                     x + 6 = 0 ;   x - 2 = 0\r\n" );
document.write( "                                         x = -6;       x = 2\r\n" );
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document.write( "Using x = -6,\r\n" );
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document.write( "a = x + 3 = -6 + 3 = -3  That's no good because we can't have a negative\r\n" );
document.write( "number for the measure of a side of a triangle.  So we discard -6, \r\n" );
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document.write( "[not because x is negative but because it produces a negative side of a\r\n" );
document.write( "triangle.  In other problems like this a negative value for x would result\r\n" );
document.write( "in only positive sides]  \r\n" );
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document.write( "Using x = 2,\r\n" );
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document.write( "a = x + 3 = 2 + 3 = 2 + 3 = 5\r\n" );
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document.write( "b = x + 10 = 2 + 10 = 12\r\n" );
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document.write( "c = x + 11 = 2 + 11 = 13\r\n" );
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document.write( "All 3 sides are positive, so x = 2 is the answer.\r\n" );
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document.write( "Edwin
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