# How do you solve #(x+7)^2= -12#?

##### 1 Answer

No solutions among *real* numbers.

Among complex numbers the two solutions are

#### Explanation:

When solving equations it is very important to define the domain of its solutions.

Are we looking for *Integer* solution? *Rational* solutions? *Real* solutions? *Complex* solutions?

Traditionally, most of the equations addressed in high school Algebra are to be solved in *real* numbers. This problem does not specify the domain, so we will consider two cases: *real_solutions and _complex* solutions.

There is no real *real*

If we expand our search for solutions to *complex* numbers, and use the classic *complex* number

which gives two solutions for

CHECK (never skip this step when solving equations!!!)