1. **State the problem:** Solve the quadratic equation $$5(x - 7)^2 = 10$$ for all values of $x$ in simplest form. 2. **Isolate the squared term:** Divide both sides of the equation by 5 to simplify. $$\cancel{5}(x - 7)^2 = \cancel{5} \times 2 \implies (x - 7)^2 = 2$$ 3. **Take the square root of both sides:** Remember to consider both the positive and negative roots. $$x - 7 = \pm \sqrt{2}$$ 4. **Solve for $x$:** Add 7 to both sides. $$x = 7 \pm \sqrt{2}$$ 5. **Final answer:** The solutions are $$x = 7 + \sqrt{2}$$ and $$x = 7 - \sqrt{2}$$. These are the simplest forms of the solutions to the given quadratic equation.