1) √(7-x) = -5
7-x = 25
x = -18

2) ∛(7-x) = -5
7-x = -125
x = 132

3) √(3x-2) + x = 4
3x-2 = (4-x)^2
3x-2 = 16-8x+x^2
x^2-11x+18 = 0
(x-2)(x-9) = 0
x = 2 or x = 9

4) ∛x-x³ = -x
x-x^3 = -x^3
2x^3-x = 0
x(2x^2-1) = 0
x = 0 or x = ±√(2)/2

5) √(2x-20) + √(x+15) = 5
2x-20 + x+15 + 2√((2x-20)(x+15)) = 25
3x-5 + 2√(2x^2-10x-300) = 25
3x - 30 = 2√(2x^2-10x-300)
3x^2 - 60x + 900 = 4(2x^2-10x-300)
3x^2 - 60x + 900 = 8x^2 - 40x - 1200
5x^2 - 20x - 2100 = 0
x^2 - 4x - 420 = 0
(x-21)(x+20) = 0
x = 21 or x = -20

6) √(x-3) = 1 + √(x-4)
x-3 = (1 + √(x-4))^2
x-3 = 1 + 2√(x-4) + (x-4)
x-3 = 2√(x-4) + x-3
0 = 2√(x-4)
0 = √(x-4)
x = 4

7) √(x+2) - √(x-6) = 2
√(x+2) = √(x-6) + 2
x+2 = x-6 + 4√(x-6) + 4
8 = 4√(x-6)
2 = √(x-6)
4 = x-6
x = 10