For the function f(x) = x² + 2x - 2, find x when f(x) = 6.

Question: For the function f(x) = x² + 2x - 2, find x when f(x) = 6.

Solution:
f(x) = x² + 2x - 2
f(x) = 6

∴ x² + 2x - 2 = 6
⇒ x² + 2x - 2 - 6 = 0
⇒ x² + 2x - 8 = 0
⇒ x² + 4x - 2x - 8 = 0
⇒ x(x + 4) - 2(x + 4) = 0
⇒ (x + 4)(x - 2) = 0
∴ x + 4 = 0 or x - 2 = 0
∴ x = - 4 or x = 2