To solve these quadratic equations, we can use the quadratic formula:

For the equation x^2 + 2x - 35 = 0:
a = 1, b = 2, c = -35

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
x = (-2 ± √(2^2 - 41(-35))) / 2*1
x = (-2 ± √(4 + 140)) / 2
x = (-2 ± √144) / 2
x = (-2 ± 12) / 2

Two possible solutions:
x1 = (-2 + 12) / 2 = 10 / 2 = 5
x2 = (-2 - 12) / 2 = -14 / 2 = -7

Therefore, the solutions for x^2 + 2x - 35 = 0 are x = 5 and x = -7.

For the equation x^2 - x - 42 = 0:
a = 1, b = -1, c = -42

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
x = (1 ± √((-1)^2 - 41(-42))) / 2*1
x = (1 ± √(1 + 168)) / 2
x = (1 ± √169) / 2
x = (1 ± 13) / 2

Two possible solutions:
x1 = (1 + 13) / 2 = 14 / 2 = 7
x2 = (1 - 13) / 2 = -12 / 2 = -6

Therefore, the solutions for x^2 - x - 42 = 0 are x = 7 and x = -6.