1. **State the problem:** Solve the equation $$0 = 3 (x - 2)^2 + 4$$ for $x$. 2. **Rewrite the equation:** $$0 = 3 (x - 2)^2 + 4$$ 3. **Isolate the squared term:** $$3 (x - 2)^2 = -4$$ 4. **Divide both sides by 3:** $$\cancel{3} (x - 2)^2 = \cancel{3} \times \left(-\frac{4}{3}\right)$$ $$ (x - 2)^2 = -\frac{4}{3}$$ 5. **Analyze the result:** The square of a real number $(x - 2)^2$ cannot be negative. Since the right side is negative, there are no real solutions to this equation. 6. **Conclusion:** The equation has no real solutions. The answer $x=2$ is not a solution to this equation. **Note:** The second expression you wrote, $$0 = 3 (x^2 + 4) \neq 7$$, is not a valid equation to solve as written, so it is ignored per instructions.