We are given the function:

$f(x) = 2\sqrt{x} + 7$

To solve $f(x) = 10$, set the function equal to 10:

$2\sqrt{x} + 7 = 10$

Step 1: Subtract 7 from both sides

$2\sqrt{x} = 10 - 7$

$2\sqrt{x} = 3$

Step 2: Divide both sides by 2

$\sqrt{x} = \frac{3}{2}$

Step 3: Square both sides to eliminate the square root

$x = \left(\frac{3}{2}\right)^2$

$x = \frac{9}{4}$

Thus, the solution is:

$x = \frac{9}{4}$

Would you like any further clarification?

Here are 5 related questions to explore:

1. What is the domain of the function $f(x) = 2\sqrt{x} + 7$?
2. How do you solve $f(x) = 15$ for the same function?
3. What happens if you apply the inverse of $f(x)$ to find $f^{-1}(10)$?
4. Can $f(x) = 2\sqrt{x} + 7$ ever be negative? Why or why not?
5. How would the graph of $f(x)$ look?

Tip: When solving square root equations, always check for extraneous solutions by substituting your result back into the original equation.