Question

How do you solve `(x+2)^2=-7`?

Answer 1

No solution

Explanation:

`(x+2)^2=-7`
`x^2+4x+4=-7`
`x^2+4x+11=0`

Now I use the discriminant to determine if there is a solution

`b^2-4ac`

`4^2-(4.7)`
`16-28`

Already, discriminant is less than zero there there are no real solutions for x.

Answer 2

`x=-2+-isqrt(7)`

Explanation:

There are many ways to tackle this; the easiest and quickest way here would be the square root method: take the square root of both sides:

`sqrt((x+2)^2)=+-sqrt(-7)`

`x+2=+-sqrt(-7)`

Since you cannot take the square root of a negative and get a real number, there is no real solution to this equation. However, we can simplify to get a complex solution:

`x+2=+-sqrt(7)*sqrt(-1)`

`x+2=+-isqrt(7)`

`x=-2+-isqrt(7)`