1. **Problem:** Solve the equation $x^{3.2} + 3.5 = 5.9$ for $x$. 2. **Step 1:** Isolate the term with $x$: $$x^{3.2} = 5.9 - 3.5$$ $$x^{3.2} = 2.4$$ 3. **Step 2:** To solve for $x$, take both sides to the power of $\frac{1}{3.2}$: $$x = (2.4)^{\frac{1}{3.2}}$$ 4. **Step 3:** Calculate the right side: $$x \approx 7.68$$ 5. **Explanation:** We used the property that if $a^b = c$, then $a = c^{1/b}$. This allows us to solve for $x$ when it is raised to a power. **Final answer:** $$x \approx 7.68$$