Square root 3x+7 + square root x+2 = 1

The answer to your question above, I will just illustrate it down.
sqrt(3 x +7 ) = 1 - sqrt(x + 2 )
square both sides:
3x + 7 = 1 -2sqrt(x = 2) + x + 2
Then it would become like this,
2x + 4 = -2sqrt( x + 2 ) 
Divide both sides by -2 to eliminate the -2 on the left side with sqrt.
Then square both sides:
x^2 + 4x + 4 = x + 2
x^2 + 3x + 2 = 0
(x + 2) (x + 1) = 0
x=-2, -1 there is no sqrt for-1
so the answer is -2