Seven less than 4 times the square of a number is 18. How do you find the number?

1 Answer
smendyka
May 23, 2018

See a solution process below:

Explanation:

"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#

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