Question

How do you solve `sqrtx+9=4`?

Answer 1

`x = O/`

Explanation:

As it stands, your equation has no possible solutions among real numbers.

To see why that is the case, isolate the radical term on one side of the equation by adding `-9` to both sides

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

`sqrt(x) = -5`

For real numbers, you have

`color(blue)(sqrt(x)>=0, (AA)x >=0)`

Simply put, the square root of a positive real number, which is what must be to begin with, is always positive.

In your case, the square root of `x` is equal to a negative number, which cannot happen for real numbers.

Therefore, your equation has no solution for any `x in RR`.