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document.write( "I wrote my first solution to this problem . . .
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document.write( "Then I saw that is was not exactly correct. Therefore, I deleted it.\r
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document.write( "Then I developed my second solution, which is in this post. Hope, it is correct.\r
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document.write( "Fist of all, since the condition does not state an opposite, I will assume that only positive branch \r\n" );
document.write( "of the square root 
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document.write( "Then the solution consists of thee steps.\r\n" );
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document.write( "1. The domain of the left side square root is the set of real numbers x >= 3.\r\n" );
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document.write( "2. The set of those \"x\" what make the right side negative is\r\n" );
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document.write( " x - 5 < 0 ====> x < 5.\r\n" );
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document.write( " Thus the set 3 <= x < 5 is the part of the solution set to the given inequality, since the left side then exist and is positive,\r\n" );
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document.write( " while the right side is negative.\r\n" );
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document.write( "3. Now we will assume that x >= 5. Then both sides of the given inequality are positive.\r\n" );
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document.write( " Square both sides. Since both sides were positive, we have a valid inequality in the domain x >= 5\r\n" );
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document.write( " x- 3 > 
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document.write( " x-3 > x^2 - 10x + 25,\r\n" );
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document.write( " 0 > x^2 - 11x + 28,\r\n" );
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document.write( " x^2 - 11x + 28 < 0,\r\n" );
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document.write( " Factor left side\r\n" );
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document.write( " (x-4)*(x-7) < 0\r\n" );
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document.write( " The solution is this interval 4 < x < 7.\r\n" );
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document.write( "Thus the final solution is the union of these sets 3 <= x < 5 and 4 < x <7.\r
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document.write( "This union is the interval 3 <= x < 7.\r
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document.write( "Thus the final ANSWER is THIS: 3 <= x < 7.\r
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document.write( "Let us check if we get the full set solution correctly.\r
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document.write( "I made this check graphically. Below please find the plots of the functions y = (red line) and the function y = x-5 (green line).\r
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document.write( "The solution set is those values of \"x\" on the x-axis, where the first plot is above the second one.\r
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document.write( " Plot of original functions y = (red) and y = x-5 (green)\r\n" );
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document.write( "Visual check confirms that the interval 3 <= x < 7 is the full set of solutions.\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
