Solve square root (2x+6)=4

For the beginning, we'll impose constraint of existence of
the square root, namely 2x+6>0.

We'll solve the
inequality:

2x+6>0

2x>-6

We'll
divide by 2:

x>-3

Now,
we'll eliminate the square root and we'll raise to square both sides of the
equation:

[sqrt( 2x + 6)]^2 =
4^2

We'll eliminate the square root from the left
side :

2x+6 = 16

We'll
subtract 6 both sides:

2x =
16-6

2x = 10

We'll divide by
2:

x = 5

Because
5>-3, the solution of the equation is x =
5.