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

Question

1442 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-11T18:41:58

$x = O/$

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 $x in RR$ .

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