Question

What are the solutions to the quadratic equation x2-16=0

Answer 1

x = -4, 4

Explanation:

Hi there!

`x^2-16=0`

Rewrite 16:

`x^2-4^2=0`

The difference of squares rule states that
`a^2-b^2=(a+b)(a-b)`. With this, apply the difference of squares to the equation:

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

The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:

`x+4=0\\x=-4`

`x-4=0\\x=4`

Therefore, the solutions are -4 and 4.

I hope this helps!