sqrt(2x+6) = 4

First we need to square both sides:

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

==> 2x + 6 = 16

==> 2x = 10

==> x = 5

Let us substitute to make sure that the function is defined for x=5:

==> sqrt(2x +6) = 4

==> sqrt(2*5+6) = 4

==> sqrt(16) = 4

==> 4= 4

Then the sloution is x= 5

To solve for x in sqrt(2x+6) = 4

sqrt(2x+6) = 4

We square both sides:

2x+6 = 4^2 = 16

2x+6 = 16.Subtract 6.

2x= 16-6 = 10

2x = 10

2x/2 = 10/2 = 5

x = 5.

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.**

The equation `sqrt (2x+6)=4` has to be solved for x

`sqrt (2x+6)=4`

First take the square of both the sides

`(sqrt (2x+6))^2=4^2`

2x + 6 = 16

Subtract 6 from both the sides

2x + 6 - 6 = 16 - 6

2x = 10

Divide both the sides by 2

(2x)/2 = 10/2

x = 5

The solution of the given equation is x = 5