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

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

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Answer 1 · 2018-05-23T18:30:00

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

1 Answer

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