To check if equation is solvable, shift 1 to the other side to form the equation:

(x+6)^1/2=-1

Next, square both side, to get this equation:

x+6= 1 Then, solve for x which equals to -5

Then, sub. x=-5 into the equation:

(-5+6)^1/2=-1 1 = -1, which is highly impossible so, equation has no solution, means complex or no roots.

To verify if (x+6)^(1/2) + 1 = 0.

Solution:

(x+6)^(1/2) + 1 = 0 . Subtract 1 from both sides:

(x+6)^(1/2) = -1. Square both sides:

x+6 = (-1)^2 = 1. Subtract 6 from both sides:

x = 1-6 = -5. The srt(-5+6) has two values -1 and +1

It is obvious that sqrt(x+6)=-1 is impossible, because sqrt(x+6) is positive, or is zero, but never negative.

First, we have to isoate the radical, by adding -1 both sides:

sqrt(x+6) = -1

Now, we'll square both sides:

x+6 = 1

We'll isolate x by adding -6:

x = 1-6

x = -5

We'll verify the solution, substituting it into the equation:

sqrt(-5+6) +1 = 0

sqrt 1 + 1 = 0

1+1 = 0

2 = 0, impossible

So x=-5 is not the solution of the equation.