How do you solve 4x2−16=0?

Step 1
${\displaystyle 4x^2-16}$
fits the difference of squares property
${\displaystyle a^2-b^2}$, which can be factored as ${\displaystyle (a+b)(a-b)}$
Here, we can take the square root of ${\displaystyle 4x^2}$ which is 2x and we can take the square root of 16 which is ${\displaystyle \pm 4}$
Thus, ${\displaystyle a=2x}$ and ${\displaystyle b=\pm 4}$, so we have
${\displaystyle (2x+4)(2x-4)=0}$
We can factor a 2 out of both expressions to get
${\displaystyle 2(x+2)(x-2)}$
Setting the factors equal to zero, we get
${\displaystyle x=\pm 2}$

Step 1
1) Add 16 to both side to get
${\displaystyle 4x^2=16}$
2) Divide both sides by 4 to get
${\displaystyle x^2=4}$
3) Find the square root of both sides to get
${\displaystyle x=\pm 2}$