"the of square of a number" -> #n^2#
"4 times the of square of a number" -> #4n^2#
"seven less than 4 times the of square of a number" -> #4n^2 - 7#
"seven less than 4 times the of square of a number is 18" -> #4n^2 - 7 = 18#
First, add #color(red)(7)# to each side of the equation to isolate the #n# term while keeping the equation balanced:
#4n^2 - 7 + color(red)(7) = 18 + color(red)(7)#
#4n^2 - 0 = 25#
#4n^2 = 25#
Next, divide each side of the equation by #color(red)(4)# to isolate the squared number while keeping the equation balanced:
#(4n^2)/color(red)(4) = 25/color(red)(4)#
#(color(red)(cancel(color(black)(4)))n^2)/cancel(color(red)(4)) = 25/4#
#n^2 = 25/4#
Now, take the square root of each side of the equation to solve for #n# while keeping the equation balanced. Remember, the square root of a number produces a positive and a negative result:
#sqrt(n^2) = +-sqrt(25/4)#
#n = +-sqrt(25)/sqrt(4)#
#n = +-5/2#
The number is #-5/2# or #5/2#