SOLUTION: Hello, I am trying to solve quadratic word problem... A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and

Question 205878: Hello, I am trying to solve quadratic word problem...
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?
Thanks
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
if you find the square grid size, you can find the number of characters

let x="first grid edge", so x+1="second grid edge"

"a square grid with equal number of rows and columns, found that 24 characters were left out."
___ x^2 + 24

"add one more row and column, he found that he was short of 25 characters"
___ (x + 1)^2 - 25

the two expressions are equal to the number of characters; and, therefore, to each other

x^2 + 24 = x^2 + 2x + 1 - 25

48 = 2x ___ 24 = x

substituting to find the number of characters ___ 24^2 + 24 = 600
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