How do you solve `2sqrt(x-11)-8=4` and check your solution?

First, add `color(red)(8)` to each side of the equation to isolate the radical term while keeping the equation balanced:

`2sqrt(x - 11) - 8 + color(red)(8) = 4 + color(red)(8)`

`2sqrt(x - 11) - 0 = 12`

`2sqrt(x - 11) = 12`

Next, divide each side of the equation by `color(red)(2)` to isolate the radical while keeping the equation balanced:

`(2sqrt(x - 11))/color(red)(2) = 12/color(red)(2)`

`(color(red)(cancel(color(black)(2)))sqrt(x - 11))/cancel(color(red)(2)) = 6`

`sqrt(x - 11) = 6`

Then square each side of the equation to eliminate the radical while keeping the equation balanced:

`(sqrt(x - 11))^2 = 6^2`

`x - 11 = 36`

Now, add `color(red)(11)` to each side of the equation to solve for `x` while keeping the equation balanced:

`x - 11 + color(red)(11) = 36 + color(red)(11)`

`x - 0 = 47`

`x = 47`

To check the solution substitute `color(red)(47)` for `color(red)(x)` in the original equation and calculate the left side of the equation to ensure it equals `4`

`2sqrt(color(red)(x) - 11) - 8 = 4` becomes:

`2sqrt(color(red)(47) - 11) - 8 = 4`

`2sqrt(36) - 8 = 4`

`(2 xx +-6) - 8 = 4`

`+-12 - 8 = 4`

`4 = 4`

Or

`-20 != 4`

The solution of `-20` is extraneous.