1. **State the problem:** Solve for $x$ in the equation $$x^2 = \sum \left( \frac{69.85 - 14}{14} \right)^2.$$ 2. **Understand the summation:** The summation symbol $\sum$ usually means adding multiple terms. However, here it looks like a single term is given inside the summation. So we assume the summation has only one term. 3. **Calculate the term inside the summation:** $$\frac{69.85 - 14}{14} = \frac{55.85}{14}.$$ 4. **Simplify the fraction:** $$\frac{55.85}{14} \approx 3.9893.$$ 5. **Square the term:** $$\left(3.9893\right)^2 = 15.9145.$$ 6. **Substitute back into the equation:** $$x^2 = 15.9145.$$ 7. **Solve for $x$ by taking the square root:** $$x = \pm \sqrt{15.9145}.$$ 8. **Calculate the square root:** $$x \approx \pm 3.9893.$$ **Final answer:** $$x \approx \pm 3.9893.$$