Question

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

Answer 1

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`