Solve sqrt(2x + 3) = x

Problem: Solve the radical equation $\sqrt{2x + 3} = x$.

Steps

1. Square both sides
   $$2x + 3 = x^2$$
2. Rearrange into standard quadratic form
   $$x^2 - 2x - 3 = 0$$
3. Factor the quadratic equation
   $$(x - 3)(x + 1) = 0$$
4. Solve for $x$
   $$x = 3 \quad \text{or} \quad x = -1$$
5. Check solutions in the original equation
   $$\text{For } x = 3: \sqrt{2(3) + 3} = \sqrt{9} = 3 \text{ (Valid)}$$
   $$\text{For } x = -1: \sqrt{2(-1) + 3} = \sqrt{1} = 1 \neq -1 \text{ (Extraneous)}$$