Question

Select all of the solutions of 4x² - 36 = 0. If there are no solutions, select the empty set. -3 -3/2 3/2 3 {}

Answer 1

Using the quadratic formula we can see the roots are:
3 and -3

Answer 2

ANSWER

The solutions are,


`x =3 \: and \: x = - 3`

Step-by-step explanation

The given equation is


`4 {x}^(2) - 36 = 0`

We factor to obtain,


`4( {x}^(2) - 9) = 0`



We rewrite to get,


`4( {x}^(2) - {3}^(2) ) = 0`

We apply difference of two squares to get,


`4(x - 3) (x + 3)= 0`

We divide through by 4 to get,



`(x - 3) (x + 3)= 0`

This implies that, either


`(x - 3) = 0 \: or \: (x + 3)= 0`
This gives,


`x =3 \: or \: x = - 3`