1. The problem is to solve the equation $$(x + 8)^2 = 39$$ for $x$. 2. We use the special quadratic equation rule: If $$x^2 = d$$, then $$x = \pm \sqrt{d}$$. 3. Applying this rule, set $$y = x + 8$$, so $$y^2 = 39$$ implies $$y = \pm \sqrt{39}$$. 4. Substitute back for $x$: $$x + 8 = \pm \sqrt{39}$$. 5. Solve for $x$: $$x = -8 \pm \sqrt{39}$$. 6. Therefore, the solutions are $$x = -8 + \sqrt{39}$$ and $$x = -8 - \sqrt{39}$$.