1. **State the problem:** We have two quadratic equations modeling wellbeing of two groups: $$x^2 + px + q = 0$$ $$x^2 + mx + k = 0$$ where $p$ = access to social services, $q$ = employment opportunities, $m$ = educational attainment and healthcare access, $k$ = safety quality. The social challenge exists if: $$(q - k)^2 = (m - p)(pk - mq)$$ 2. **Understand the condition:** This equation relates parameters of both groups. To identify if the social challenge exists, we check if the above equality holds true for given values of $p, q, m, k$. 3. **Analyze the expression:** Expand the right side: $$(m - p)(pk - mq) = m \, pk - m \, mq - p \, pk + p \, mq$$ 4. **Rewrite the right side:** $$= m p k - m m q - p p k + p m q$$ 5. **Interpretation:** The left side $(q-k)^2$ is a square of difference in employment and safety quality. The right side involves products and differences of social service access, education, employment, and safety. 6. **Conclusion:** Without specific numeric values for $p, q, m, k$, we cannot definitively say if the equality holds. **Therefore, as a data analyst, you must plug in the actual data values for $p, q, m, k$ into the equation:** $$ (q-k)^2 \stackrel{?}{=} (m-p)(pk - mq) $$ If true, the common social challenge exists; if false, it does not. **Final answer:** The existence of the common social challenge depends on whether the given equality holds for the specific data values of $p, q, m, k$.