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,

$x =3 \: and \: x = - 3$

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,

$x =3 \: or \: x = - 3$