Algebra.Com's Answer #852398 by ikleyn(52884)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A square has an area of x^2 + 6x + 9. Find the length of a side. Make a sketch of the square Please help
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document.write( " Tutor @Theo' solution is many words.\r
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document.write( " I don't like toooo wordy solutions: I think that too wordy explanations are bad style to teach Math. \r
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document.write( " So, I will write another solution, much shorter and, I believe, more educative.\r
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document.write( "The expression x^2 + 6x + 9 represents an algebraic perfect square  .\r\n" );
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document.write( " So, the area of the square is square units.\r\n" );
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document.write( "Hence, the side length of this square is square root of this perfect square .\r\n" );
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document.write( "So, our first desire is to declare that the side length is (x+3) units.\r\n" );
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document.write( "But it would be too hastily and not always correct.\r\n" );
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document.write( "The reason is that this expression (x+3) can be negative, since we don't know what 'x' is.\r\n" );
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document.write( "Meanwhile, the length of the square must be positive due to the meaning of this notion/conception.\r\n" );
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document.write( "Therefore, more accurate is to write  = |x+3| , using the absolute value.\r\n" );
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document.write( "This form is universally correct for all possible values of 'x'.\r\n" );
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document.write( "ANSWER. If the area of a square is x^2 + 6x + 9 square units, then the side of the square is |x+3| units.\r\n" );
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document.write( "Solved, with complete explanations in compact form.\r
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