1. The problem is to solve the equation $x^2 + 12 = 76$ for $x$. 2. The formula used here is to isolate $x^2$ by subtracting 12 from both sides: $$x^2 + 12 - 12 = 76 - 12$$ 3. Simplify both sides: $$x^2 = 64$$ 4. To solve for $x$, take the square root of both sides: $$x = \pm \sqrt{64}$$ 5. Calculate the square root: $$x = \pm 8$$ 6. Therefore, the solutions are: $$x = 8 \text{ or } x = -8$$ This means $x$ can be either 8 or -8 to satisfy the equation.