To complete the square you halve the coefficient of the x term and square it. Half of 14 is 7 and 7² is 49. So we add 49 and subtract 49, which means we are not changing the value of the quadratic. So we have x²+14x+49-49+2. This can be written: (x²+14x+49)-49+2, which is (x+7)²-47, which is answer a.
