1. **State the problem:** Given the function $f(x) = 4\sqrt{x} + 3$, solve for $x$ when $f(x) = 10$. 2. **Set up the equation:** $$4\sqrt{x} + 3 = 10$$ 3. **Isolate the square root term:** $$4\sqrt{x} = 10 - 3$$ $$4\sqrt{x} = 7$$ 4. **Divide both sides by 4:** $$\cancel{4}\sqrt{x} = \frac{7}{\cancel{4}}$$ $$\sqrt{x} = \frac{7}{4}$$ 5. **Square both sides to eliminate the square root:** $$\left(\sqrt{x}\right)^2 = \left(\frac{7}{4}\right)^2$$ $$x = \frac{49}{16}$$ 6. **Final answer:** $$x = \frac{49}{16}$$ This is the exact solution for $x$ when $f(x) = 10$.