Verified answer

Assume it equals -1 to get boundaries.

√x - √(x+5) = -1

Add 1 to both sides and add √(x + 5) to both sides to isolate the √(x + 5):

1 + √x = √(x + 5)

Square both sides; left side is FOIL, (1 + √x)(1 + √x)

1 + 2√x + x = x + 5

Add -1 and -x to both sides to isolate 2√x

2√x = 4

Square both sides again

4x = 16

so x = 4 is the boundary. Try x = 5 and see if it works

√5 - √10 = -0.9 so false

Try x = 3

√3 - √8 = -1.09 so true

and since you can't √ a negative, you know x ≥ 0

so the answer is 0 ≤ x < 4

ah, I think that there is a mistake in the formatting somewhere as √x-√x = 0

0 < -1 -5

0 < -6

and this is clearly not true