Before we proceed with solving each equation, let's first determine the solutions to each of the given equations:

1) x² = 42
x = √42
x ≈ ±6.48

2) 14 + y² = 25
y² = 25 - 14
y² = 11
y = ±√11

3) a² = 5.19
a = √5.19
a ≈ ±2.28

4) x² = 0.0204
x = √0.0204
x ≈ ±0.14

5) 20 + x² = 56
x² = 56 - 20
x² = 36
x = ±√36
x = ±6

6) 2y² = 50
y² = 50 / 2
y² = 25
y = ±√25
y = ±5

7) a² - 1 = 4.29
a² = 4.29 + 1
a² = 5.29
a = √5.29
a ≈ ±2.30

8) b² - 3 = 1.84
b² = 1.84 + 3
b² = 4.84
b = √4.84
b ≈ ±2.20

These are the solutions to each of the given equations.