Question: User: $x^2+3=0$
1. **State the problem:** Solve the quadratic equation $$x^2 + 3 = 0$$.
2. **Formula and rules:** To solve for $x$, isolate $x^2$ and then take the square root of both sides. Remember that the square root of a negative number involves imaginary numbers.
3. **Isolate $x^2$:**
$$x^2 = -3$$
4. **Take the square root of both sides:**
$$x = \pm \sqrt{-3}$$
5. **Simplify the square root of a negative number:**
$$x = \pm \sqrt{-1 \times 3} = \pm \sqrt{-1} \times \sqrt{3} = \pm i\sqrt{3}$$
6. **Final answer:**
$$x = \pm i\sqrt{3}$$
This means the solutions are purely imaginary numbers.