What is the solution of equation [square root(4x+8)] - x=3?

We'll start by imposing the constraints of existence of
square root:

4x + 8 >=
0

We'll subtract 8:

4x
>= -8

x >=
-2

The interval of admissible values for x is: [-2 ,
+infinite).

We'll shift x to the right, to isolate the
square root to the left.

Now, we'll solve the equation
raising to square both sides:

4x + 8 =
(x+3)^2

We'll expand the square from the right
side:

4x + 8 = x^2 + 6x +
9

We'll shift all terms to the right side and then we'll
apply the symmetric property:

x^2 + 6x + 9 - 4x - 8 =
0

We'll combine like
terms:

x^2 + 2x + 1 = 0

We'll
recognize a perfect square:

(x+1)^2 =
0

x1 = x2  =
-1

Since the value of x belongs to the range
[-2 , +infinite), we'll accept it as solution of the equation: x =
-1.