Question

The square of 9 less than a number is 3 less than the number. What is the number

Answer 1

Answer: d. 7 or 12

Explanation:

Answer 2

7 or 12

Explanation:

Write the words into a math expression converting these words into symbols:

• Is =
• Square (n)^2
• Number n
• less than -

The square of 9 less than a number can be written as
`(n-9)^2`.

Is 3 less than a number can be written as (n-3).

Set them equal and solve for n by factoring.

`(n-9)^2=n-3\\n^2-18n+81=n-3\\n^2-19n+84=0\\(n-7)(n-12)=0\\`

To solve for n, set each factor equal to 0 through the zero product property.

n-7=0 so n=7.

n-12=0 so n=12.