Question

How do you solve `4x^2 - 16 = 0`?

Answer 1

`x = +-2`

Explanation:

1. Add `16` to both sides to get `4x^2=16`
2. Divide both sides by `4` to get `x^2=4`
3. Find the square root of both sides to get `x = +-2`

Answer 2

`x=+-2`

Explanation:

`4x^2-16` fits the difference of squares property

`a^2-b^2`, which can be factored as `(a+b)(a-b)`

Here, we can take the square root of `4x^2`, which is `2x` and we can take the square root of `16` which is `+-4`.

Thus, `a=2x` and `b=+-4`, so we have

`(2x+4)(2x-4)=0`

We can factor a `2` out of both expressions to get

`2(x+2)(x-2)`

Setting the factors equal to zero, we get

`x=+-2`

Hope this helps!