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