Problem 8 - Entrance Test

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x by factoring, completing the square, or using the quadratic formula. The quadratic formula is x = [-b ± sqrt(b^2-4ac)]/(2a). For the equation x^2 + 2x - 6 = 0, a = 1, b = 2, and c = -6. Plugging these values into the formula gives x = [-2 ± sqrt(2^2 - 4*1*(-6))]/(2*1) = [-2 ± sqrt(4 + 24)]/2 = [-2 ± sqrt(28)]/2 = [-2 ± sqrt(4*7)]/2 = [-2 ± 2*sqrt(7)]/2 = -1 ± sqrt(7). Thus, the solutions are -1 + sqrt(7) and -1 - sqrt(7), which does not directly match any provided choices, indicating a misunderstanding in directly applying the quadratic formula towards the given options.