Question

How do you solve `\sqrt { 4- x } - 5= 9`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(5)` to each side of the equation to isolate the radical while keeping the equation balanced:

`sqrt(4 - x) - 5 + color(red)(5) = 9 + color(red)(5)`

`sqrt(4 - x) - 0 = 14`

`sqrt(4 - x) = 14`

Next, square both sides of the equation to eliminate the radical while keeping the equation balanced:

`(sqrt(4 - x))^2 = 14^2`

`4 - x = 196`

Then, subtract `color(red)(4)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(4) + 4 - x = -color(red)(4) + 196`

`0 - x = 192`

`-x = 192`

Now, multiply each side of the equation by `color(red)(-1)` to solve for `x` while keeping the equation balanced:

`color(red)(-1) xx -x = color(red)(-1) xx 192`

`x = -192`

Answer 2

`x = -192`

Explanation:

`sqrt(4-x)=9+5`
Squaring both sides,
`4-x = 196`
`x= 4-196=-192`