'Simplest surd form' is a clue that quadratic factorising will not work for this question, so we must instead use the quadratic formula. It is always a good idea to quote this as marks are often available for quoting formulae.
x = [-b±√(b^2-4ac)]/2a where ax^2 + bx + c = 0
Thus, a = 1, b = 2, c = -4
Sub this data into the formula:
[-2 ± √2^2 - (4 x 1 x -4)] / (2x1)
This question is non-calculator, so simplify down to get
[-2 ± √(4 + 16)] / 2
[-2 ± √20 ] / 2
√20 can be simplified (important as the question states in simplest surd form)
√20 = √5√4 = 2√5
[-2 ± 2√ 5] / 2
Thus x = -1 ± √5