document.write( "Question 143952: A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
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Algebra.Com's Answer #104748 by stanbon(75887) $\"\"$ $\"About$

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A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
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\n" ); document.write( "Let the number of rows/columns in the 1st square be \"x\".
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\n" ); document.write( "EQUATIONS:
\n" ); document.write( "# of characters = x^2+24
\n" ); document.write( "# of characters = (x+1)(x+1)-25
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\n" ); document.write( "x^2+24 = (x+1)^2-25
\n" ); document.write( "x^2+24 = x^2+2x+1-25
\n" ); document.write( "24 = 2x-24
\n" ); document.write( "2x = 48
\n" ); document.write( "x = 24
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\n" ); document.write( "# of characters = 24^2 = 576
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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