Question

How do you use square roots to solve `2(x+3)^2=8`?

Answer 1

`x=-1,-5`

Explanation:

Our first step would be to divide both sides by `2`. We get:

`(x+3)^2=4`

We can take the `+-` square root of both sides, and we will now have two equations:

The first:
`x+3=2`

`color(blue)(=>x=-1)`

The second:
`x+3=-2`

`color(blue)(=>x=-5)`

We have two equations because we need to take the `+-` square root of both sides, because when you take the sqrt of a number, there will always be a positive and a negative answer.

Hope this helps!

Answer 2

Express the answer with surds, it's not possible here as the surd is a perfect square.

Explanation:

So

`2(x+3)^2 = 8`

`(x+3)^2 = 4`

`(x+3) = +- sqrt4`
`x = +- 2 - 3`