```Question 139177
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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Translating this statement into an equation
"A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of row and columns, found that 24 characters were left out."
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If x = number of characters in each row and column
we translate this statement as
x*x + 24 = total number of characters
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"When he tried to add one more row and column, he found that he was short of 25 characters."
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Now, the number of rows is "x + 1", and the number of columns is "x + 1", so we have
(x + 1)(x + 1) - 25 = total number of characters.
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FOIL above and write an equation from the two grids
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2nd grid = 1st grid
x^2 + 2x + 1 -25 = x^2 + 24
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x^2 + 2x -24 = x^2 + 24
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x^2 - x^2 + 2x - 24 - 24 = 0
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2x - 48 = 0
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2x = +48
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x = 48/2
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x = 24
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Grid is 24 by 24 which contains 576 character + 24 left out = 600 Characters
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Grid of 25 by 25 = 625 character so he would have 25 blanks
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Did this make sense to you? Any questions?

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