Set 13: Quadratic Equations

Choice A is correct. Choice A is the correct answer. 1. Square both sides: $2x + 3 = x^2$. 2. Rearrange: $x^2 - 2 x - 3 = 0$. 3. Factor: $(x - 3)(x + 1) = 0$. 4. Potential roots: $3, -1$. 5. Check: $\sqrt{2(3)+3} = \sqrt{9} = 3$ (Matches x). $\sqrt{2(-1)+3} = \sqrt{1} = 1 \neq -1$. So -1 is extraneous. Choice B is incorrect because -1 is extraneous. Choice C is incorrect. Choice D is incorrect.