1. **State the problem:** Solve the equation $x^2 + 1 = 5$ for $x$. 2. **Use the formula:** To solve for $x$, isolate $x^2$ by subtracting 1 from both sides: $$x^2 = 5 - 1$$ 3. **Simplify:** $$x^2 = 4$$ 4. **Solve for $x$:** Take the square root of both sides. Remember, the square root of a number has two values, positive and negative: $$x = \pm \sqrt{4}$$ 5. **Evaluate the square root:** $$x = \pm 2$$ 6. **Final answer:** The solutions to the equation are: $$x = 2 \text{ or } x = -2$$