The equation to be solved is x=(x+6)^1/2

x=(x+6)^1/2

square both the sides

=> x^2 = x + 6

=> x^2 - x - 6 = 0

=> x^2 - 3x + 2x - 6 = 0

=> x(x - 3) + 2(x - 3) = 0

=> (x + 2)(x - 3) = 0

=> x = 3 and x = -2

**The solution of the equation is x = 3 and x = -2**

The equation x=(x+6)^1/2 has to be solved.

x=(x+6)^1/2

Take the square of both the sides

x^2 = x + 6

Solve the quadratic equation obtained.

x^2 - x - 6 = 0

x^2 - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = -2 and x = 3

Both of these solutions satisfy the given equation as the square root of a positive number can be negative,

We'll eliminate the square root from the right side. For this reason, we'll square both sides.

x^2 = [(x+6)^1/2]^2

x^2 = x + 6

We'll subtract x + 6 both sides:

x^2 - x - 6 = 0

We'll factorize and we'll get:

(x - 3)(x + 2) = 0

x - 3 = 0

x = 3

x + 2 = 0

x = -2

We'll verify the values of x in the equation:

x = 3

3 = sqrt(3+6)

3 = sqrt9

3 = 3

x = -2

-2 = sqrt(-2+6)

-2 = sqrt4

-2 is different from 2.

So, we'll reject the solution x = -2.

**The only solution of the equation is x = 3**