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

2 Answers
Mar 25, 2018

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.

Mar 25, 2018

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)