1. **State the problem:** Solve the equation $$\frac{5x^2}{2} + 47 = 137$$ for $x$. 2. **Isolate the term with $x^2$:** Subtract 47 from both sides: $$\frac{5x^2}{2} = 137 - 47$$ $$\frac{5x^2}{2} = 90$$ 3. **Eliminate the fraction:** Multiply both sides by 2: $$5x^2 = 180$$ 4. **Solve for $x^2$:** Divide both sides by 5: $$x^2 = \frac{180}{5} = 36$$ 5. **Find $x$:** Take the square root of both sides: $$x = \pm \sqrt{36} = \pm 6$$ **Final answer:** $$x = 6 \text{ or } x = -6$$