Question

PLEEAASSEE HELP!!!

The square of a number exceeds that number by 12. What are the two possible solutions?

3 or -4
3 or 4
-3 or 4

Please explain if you can!!

Answer 1

Let's call the number x. The square of a number would be
`x^(2)`. This is 12 more than the number itself. 12 more than the number is 12+x.

Putting this together we get
`x^(2) =x+12`
This is a quadratic equation so we set it equal to zero by subtracting x+12 from both sides. We obtain:


`x^(2) -x-12=0`

The left-had side factors as such:
(x-4)(x+3)=0

Since we have two expressions that when multiplied give zero either one or both equal zero. We set each equal to zero to obtain the solutions:

`x-4=0` so x =4
and

`x+3=0` so x=-3

The two solutions are 4 and -3