Set 1: Quadratic Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. The area of a square is given by $s^2$. We need to write the quadratic expression as a perfect square. 1. Check if $x^2 + 14 x + 49$ is a perfect square. 2. Half of 14 is 7. $7^2 = 49$. It matches. 3. Factor: $(x + 7)^2$. Thus, the side length $s$ is $x + 7$. Choice B is incorrect because the middle term is positive, so the factor must be $(x+7)$, not $(x-7)$. Choice C is incorrect because $(x+14)^2 = x^2 + 28 x + 196$. Choice D is incorrect because it is not the square root of the constant.